Measure-Theory

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数学英语专业词汇

数学专业英语词汇(A)/bbsxp/dispbbs.asp?boardID=28&ID=2889数学专业英语词汇(B)b measurability b可测性b measurable function 波莱尔可测函数babylonian numerals 巴比伦数字back substitution 逆计算backward difference 后向差分backward difference operator 后向差分算子backward difference quotient 后向差商backward solution 后向解法baire function 贝利函数baire measure 贝利测度baire set 贝利集baire space 贝利空间baire theorem 贝利定理balance 平衡balanced category 平衡范畴balanced functor 平衡函子balanced hypergraph 平衡超图balanced neighborhood 平衡邻域balanced sample 平衡样本balanced set 平衡集balancing method 平衡法balayage 扫除ball 球ballistic curve 弹道banach algebra 巴拿赫代数banach lie group 巴拿赫李群banach space 巴拿赫空间band 带band chart 带状图band matrix 带状矩阵bar construction 棒构成bar diagram 条线图bar graph 条线图barrel 桶集barrel shape 桶型barrelled space 桶型空间barrier 闸barycenter 重心barycenter of a simplex 单形的重心barycentric 重心的barycentric complex 重心复形barycentric coordinates 重心坐标barycentric mapping 重心映射barycentric subdivision 重心重分base 底base angle 底角base line 底线base number 底数base of logarithms 对数的底base point 基点base register 基址寄存器变址寄存器base space 底空间base vector 基向量basic 基础的basic block 基本块basic field 基域basic form 基本形式basic point 基础点basic representation 基本表示basic ring 基环basic solution 基本解basic symbol 基本符号basic variable 基本变量basis 基basis for cohomology 上同爹basis for homology 同爹basis of linear space 线性空间的基basis of vector space 向量空间的基basis replacement procedure 基替换过程basis theorem of hilbert 希耳伯特基定理basis vector 基本向量batch processing 成批处理bayes decision function 贝叶斯判定函数bayes formula 贝叶斯公式bayes postulate 贝叶斯公设bayes solution 贝叶斯解behavior 行为behavior strategy 行为策略bellman principle 贝尔曼原理beltrami equation 贝尔特拉米方程bending point 转向点bergman metric 伯格曼度量bernoulli equation 伯努利方程bernoulli inequality 伯努利不等式bernoulli method 伯努利法bernoulli number 伯努利数bernoulli polynomial 伯努利多项式bernoulli trials 伯努利试验bernoullian polynomial 伯努利多项式bernstein inequality 伯思斯坦不等式bernstein polynomial 伯思斯坦多项式bertrand curves 柏特龙曲线bertrand paradox 柏特龙悖论bessel equation 贝塞耳方程bessel function 贝塞耳函数bessel function of the second kind 第二类贝塞耳函数bessel function of the third kind 第三类贝塞耳函数bessel inequality 贝塞耳不等式bessel integral 贝塞耳积分best approximation 最佳逼近best estimator 最佳估计量best test 最佳检验best uniform approximation 最佳一致逼近beta distribution 分布beta function 函数betti group 贝蒂群betti number 贝蒂数between group variance 群间方差biadditive 双加法的biangular 双角的bias 偏倚biased estimator 有偏估计量biased sample 有偏样本biased statistics 有偏统计量biased test 有偏检验biaxial 双轴的biaxial spherical harmonic function 双轴球面低函数bicartesian square 双笛卡儿方bicharacteristic 双特征bicompact 紧bicompact set 紧集bicompact space 列紧空间bicompact transformation group 列紧变换群bicompactification 紧化bicomplex 二重复形bicomplex function 二重复形函数biconcave 两面凹的biconditional 等价biconnected space 双连通空间bicontinuous function 双连续函数bicontinuously differentiable 双连续可微bicylinder 双圆柱bidimensional 二维的bidimensionality 二维性bidual banach space 双对偶巴拿赫空间bifunctor 二变项函子bifurcation point 歧点bifurcation theory 分歧理论bigraded group 双重分次群bigraded module 双重分次模biharmonic 双低的biharmonic equation 双低方程biharmonic function 双低函数biholomorphic 双全纯的biholomorphic function 双正则函数biholomorphic mapping 双正则映射bihomomorphism 双同态bijection 双射bijective mapping 双射bijectivity 双射性bilateral 两面的bilateral derivative 双侧导数bilateral laplace transform 双侧拉普拉斯变换bilaterally bounded sequence 双侧有界序列bilinear 双线性的bilinear form 双线性形式bilinear functional 双线性泛函bilinear integral form 双线性积分型bilinear mapping 双线性映射bilinear programming 双线性规划bilinear relation 双线性关系bilinear system 双线性系bilinear transformation 双线性变换bilinearity 双线性bimatrix game 双矩阵对策bimodal distribution 双峰分布bimodule 双模binary 二元的binary arithmetic 二进制算术binary code 二进制吗binary coded decimal notation 二进制编码的十进记数法binary coded decimal system 二进制编码的十进制binary coding 二进制编码binary digit 二进制数字binary digital computer 二进制数字计算机binary element 双态元件binary number 二进制数binary number system 二进制数系binary operation 二元运算binary point 二进制小数点binary relation 二元关系binary system 二进制的binary translation 二进制变换bind 连结binomial 二项式binomial coefficient 二项式系数binomial differential 二项式微分binomial differential equation 二项微分方程binomial distribution 二项分布binomial equation 二项方程binomial expansion 二项展开式binomial integral 二项式积分binomial probability paper 二项式概率纸binomial series 二项级数binomial surd 二项不尽根binomial test 二项检验binomial theorem 二项式定理binormal 副法线binormal space 副法线空间binormal vector 副法线向量biodemography 生物人口统计学biomathematic 生物数学的biomathematics 生物数学biomechanics 生物力学biometrics 生物统计学biometrika 生物统计学biophysics 生物物理学biorthogonal system 双正交系biorthonormal expansion 双标准正交展开biorthonormalization 双标准正交化bipartite cubic 双枝三次曲线bipartite graph 偶图bipolar 双极的bipolar coordinates 双极坐标bipolar theorem 双极定理biprism 双棱柱biquadrate 四次方biquadratic equation 双二次方程biquadratic residue 双二次剩余biquaternion 复四元数biquinary code 二元五元码birational 双有理的birational invariant 双有理不变量birational map 双有理映射birational transformation 双有理变换birectangular 两直角的biregular 双正则的biregular isomorphism 双正则同构birth process 出生过程birth rate 出生率bisect 平分bisecting point 平分点bisection 平分bisector 平分线bisector of angle 角的平分线bispherical 双球面的bispinor 双旋量bistable 双稳定的bisymmetry 双对称bit 比特bitangent 双切线biunique 一对一的bivalent 二价的bivariate distribution 二维分布bivariate distribution function 二元分布函数bivariate frequency function 二元频率函数bivariate normal distribution 二元正态分布bivariate population 二元总体bivector 二重向量block 块block design 区组设计block relaxation 块松弛block tridiagonal matrix 块三对角阵blockdiagram 立体图bochner integral 博赫纳积分body 体body of revolution 旋转体boltzmann constant 玻耳兹曼常数boltzmann equation 玻耳兹曼方程boltzmann statistics 玻耳兹曼统计bolzano weierstrass theorem 波尔察诺维尔斯特拉斯定理boole function 布尔函数boolean algebra 布尔代数boolean function 布尔函数boolean operation 布尔运算boolean optimization 布尔最优化boolean ring 布尔环boolean vector 布尔向量border 边缘border element 边缘元素border of the domain 域的边缘border set 边缘集bordered matrix 加边矩阵borel exceptional value 波莱尔例外值borel field 波莱尔域borel group 波莱尔群borel lebesgue covering theorem 波莱尔勒贝格覆盖定理borel measurable function 波莱尔可测函数borel measure 波莱尔测度borel set 波莱尔集borel subgroup 波莱尔子群borel summable series 波莱尔可和级数born approximation 波饵似法bornological dual 有界型对偶bornological set 有界型集bornological space 有界型空间bornological topology 有界型拓扑学bornology 有界型性bott periodicity theorem 博特周期性定理bound 界bound decision variable 约束决策变量bound term 约束项bound variable 约束变词boundary 边界;边缘boundary cell 边界胞腔boundary collocation 边界配置boundary condition 边界条件boundary correspondence 边界对应boundary curve 边界曲线boundary element method 边界元法boundary form 边缘形式boundary homomorphism 边缘同态boundary interval 边界区间boundary layer 边界层boundary line 界线boundary method 边界法boundary operator 边缘算子boundary point 边界点boundary simplex 边界单形boundary strip 边界带boundary surface 带边界曲面boundary value 边界值boundary value problem 边值问题bounded 有界的bounded above 上有界的bounded above sequence 上有界序列bounded below 下有界的bounded below sequence 下有界序列bounded chain 有界链bounded closed set 有界闭集bounded domain 有界域bounded existential quantifier 有界存在量词bounded function 有界函数bounded matrix 有界矩阵bounded minimization 有界最小化bounded operator 有界算子bounded point sequence 有界点序列bounded quantification 有界量词限制bounded quantifier 有界量词bounded sequence 有界序列bounded set 有界集合bounded to the downwards 下有界的bounded to the upwards 上有界的bounded variation 有界变分boundedly convergent series 有界收敛级数boundedness 有界性bounding manifold 边界廖bounding surface 边界曲面boundless 无限的box 框brace 大括号brachistochrone 最速降线brachistochrone problem 最速降线问题bracket 括号bracket operation 括号运算bragg curve 布喇格曲线braid 辫braid group 辫群branch 分支branch and bound method 分支限界法branch curve 分枝曲线branch cut 分支切割branch divisor 分歧除子branch instruction 分枝指令branch line 分枝线branch of a curve 曲线的分枝branch of function 函数的分枝branch point 分枝点branching 分枝branching process 分枝过程brauer group 布劳韦尔群breadth 幅break point 断点;分割点break point instruction 断点指令breaking stress 破坏应力bridge 分离棱briggs' logarithm 常用对数briggsian logarithm 常用对数broken diagonal 折对角线broken line 折线broken number 分数brouwer fixed point theorem 布劳丰尔不动点定理brownian motion 布朗运动brownian movement 布朗运动bruhat decomposition 布鲁阿分解buckling 弯曲budget 顸算buffer 缓冲器bundle 束bundle map 丛映射bundle of coefficients 系数丛bundle of lines 线把bundle of p vectors 向量丛bundle of planes 平面把bundle of rays 线把bundle of spheres 球把bundle space 丛空间bundle structure theorem 丛结构定理bus 母线byte 字节[此贴子已经被作者于06-06-05 11:39:26编辑过]2006-5-12 11:48:00王焱钢琴网组织的珠江钢琴团购正在火热进行，点击查看详情风轻云淡头衔：副管理员等级：超级版主威望：9文章：5337积分：33083注册：2004年12月31日第 2 楼c function c 类函数c manifold c 廖c mapping c 类映射ca set 上解析集calculability 可计算性calculable mapping 可计算映射calculable relation 可计算关系calculate 计算calculating automaton 计算自动机calculating circuit 计算电路calculating element 计算单元calculating machine 计算机calculating punch 穿孔计算机calculating register 计算寄存器calculating unit 计算装置calculation 计算calculation of areas 面积计算calculator 计算机calculus 演算calculus of approximations 近似计算calculus of classes 类演算calculus of errors 误差论calculus of finite differences 差分法calculus of probability 概率calculus of residues 残数计算calculus of variations 变分法calibration 校准canal 管道canal surface 管道曲面cancel 消去cancellation 消去cancellation law 消去律cancellation property 消去性质cancelling of significant figures 有效数字消去canonical basis 典范基canonical coordinates 标准坐标canonical correlation coefficient 典型相关系数canonical decomposition 标准分解canonical distribution 典型分布canonical ensemble 正则总体canonical equation 典型方程canonical equation of motion 标准运动方程canonical expression 典范式canonical factorization 典范因子分解canonical flabby resolution 典型松弛分解canonical form 标准型canonical function 标准函数canonical fundamental system 标准基本系统canonical homomorphism 标准同态canonical hyperbolic system 典型双曲线系canonical image 标准象canonical mapping 标准映射canonical representation 典型表示canonical sequence 标准序列canonical solution 标准解canonical system of differential equations 标准微分方程组canonical variable 典型变量canonical variational equations 标准变分方程canonical variational problem 标准变分问题cantor curve 康托尔曲线cantor discontinum 康托尔密断统cantorian set theory 经典集论cap 交cap product 卡积capacity 容量card 卡片card punch 卡片穿孔机card reader 卡片读数器cardinal 知的cardinal number 基数cardinal product 基数积cardioid 心脏线carrier 支柱carry 进位carry signal 进位信号cartan decomposition 嘉当分解cartan formula 嘉当公式cartan subalgebra 嘉当子代数cartan subgroup 嘉当子群cartesian coordinate system 笛卡儿坐标系cartesian coordinates 笛卡尔座标cartesian equation 笛卡儿方程cartesian folium 笛卡儿叶形线cartesian product 笛卡儿积cartesian space 笛卡儿空间cartography 制图学cascaded carry 逐位进位casimir operator 卡巫尔算子cassini oval 卡吾卵形线casting out 舍去casting out nines 舍九法catastrophe theory 突变理论categorical judgment 范畴判断categorical proposition 范畴判断categorical syllogism 直言三段论categorical theory 范畴论categoricity 范畴性category 范畴category of groups 群范畴category of modules 模的范畴category of sets 集的范畴category of topological spaces 拓扑空间的范畴catenary 悬链线catenary curve 悬链线catenoid 悬链曲面cauchy condensation test 柯微项收敛检验法cauchy condition for convergence 柯握敛条件cauchy criterion 柯握敛判别准则cauchy distribution 柯沃布cauchy filter 柯嗡子cauchy inequality 柯位等式cauchy integral 柯锡分cauchy integral formula 柯锡分公式cauchy kernel 柯嗡cauchy kovalevskaya theorem 柯慰仆吡蟹蛩箍ǘɡ眵cauchy mean value formula 广义均值定理cauchy net 柯硒cauchy principal value 柯蔚cauchy problem 柯问题cauchy process 柯锡程cauchy residue theorem 残数定理cauchy sequence 柯悟列causal relation 因果关系causality 因果律cause 原因cavity 空腔cavity coefficient 空胴系数cayley number 凯莱数cayley sextic 凯莱六次线cayley transform 凯莱变换ccr algebra ccr代数celestial body 天体celestial coordinates 天体坐标celestial mechanics 天体力学cell 胞腔cell complex 多面复形cellular approximation 胞腔逼近cellular automaton 细胞自动机cellular cohomology 胞腔上同调cellular cohomology group 胞腔上同岛cellular decomposition 胞腔剖分cellular homotopy 胞腔式同伦cellular map 胞腔映射cellular subcomplex 胞腔子复形center 中心center of a circle 圆心center of curvature 曲率中心center of expansion 展开中心center of force 力心center of gravity 重心center of gyration 旋转中心center of inversion 反演中心center of mass 质心center of pressure 压力中心center of principal curvature 助率中心center of projection 射影中心center of symmetry 对称中心centered process 中心化过程centered system of sets 中心集系centi 厘centigram 厘克centimetre 厘米central angle 圆心角central confidence interval 中心置信区间central conic 有心圆锥曲线central derivative 中心导数central difference 中心差分central difference operator 中心差分算子central divided difference 中心均差central element 中心元central extension 中心扩张central extension field 中心扩张域central limit theorem 中心极限定理central line 中线central moment 中心矩central point 中心点central processing unit 中央处理器central projection 中心射影central quadric 有心二次曲面central series 中心群列central symmetric vector field 中心对称向量场central symmetry 中心对称centralizer 中心化子centre 中心centre of a circle 圆心centre of gyration 旋转中心centre of projection 射影中心centre of similarity 相似中心centre of similitude 相似中心centrifugal force 离心力centripetal acceleration 向心加速度centroid 形心certain event 必然事件certainty 必然cesaro mean 纬洛平均cesaro method of summation 纬洛总求法chain 链chain complex 链复形chain condition 链条件chain equivalence 链等价chain equivalent 链等价的chain group 链群chain homotopic 链同伦的chain homotopy 链同伦chain index 链指数chain map 链变换chain of prime ideals 素理想链chain of syzygies 合冲链chain rule 链式法则chain transformation 链变换chainette 悬链线chamber complex 箱盒复形chance 偶然性;偶然的chance event 随机事件chance move 随机步chance quantity 随机量chance variable 机会变量change 变化change of metrics 度量的变换change of the base 基的变换change of the variable 变量的更换channel 信道channel width 信道宽度character 符号character group 特贞群character space 特贞空间characteriatic system 特寨characteristic 特征characteristic boundary value problem 特者值问题characteristic class 示性类characteristic cone 特斩characteristic conoid 特沾体characteristic curve 特怔线characteristic derivation 特阵导characteristic determinant 特招列式characteristic differential equation 特闸分方程characteristic direction 特战向characteristic equation 特战程characteristic exponent 特崭数characteristic function 特寨数characteristic functional 特蘸函characteristic group 特蘸characteristic index 特崭标characteristic initial value problem 特挣值问题characteristic linear system 特者性系统characteristic manifold 特瘴characteristic matrix 特肇阵characteristic number 特正characteristic of a logarithm 对数的首数characteristic parameter 特瘴数characteristic polynomial 特锗项式characteristic pontrjagin number 庞德里雅金特正characteristic root 特争characteristic ruled surface 特毡纹曲面characteristic series 特招characteristic set 特寨characteristic state 特宅characteristic strip 特狰characteristic subgroup 特沼群characteristic surface 特怔面characteristic value 矩阵的特盏characteristic vector 特镇量charge 电荷chart 图chebyshev function 切比雪夫函数chebyshev inequality 切比雪夫不等式chebyshev polynomial 切比雪夫多项式check 校验check digit 检验位check routine 检验程序check sum 检查和chevalley group 歇互莱群chi square distribution 分布chi squared test 检验chi squared test of goodness of fit 拟合优度检验choice function 选择函数chord 弦chord line 弦chord of contact 切弦chord of curvature 曲率弦chordal distance 弦距离christoffel symbol 克里斯托弗尔符号chromatic number 色数chromatic polynomial 色多项式cipher 数字circle 圆circle diagram 圆图circle method 圆法circle of contact 切圆circle of convergence 收敛圆circle of curvature 曲率圆circle of inversion 反演圆circle problem 圆内格点问题circuit free graph 环道自由图circuit rank 圈数circulant 循环行列式circulant matrix 轮换矩阵circular 圆的circular arc 圆弧circular cone 圆锥circular correlation 循环相关circular cylinder 圆柱circular disk 圆盘circular domain 圆形域circular frequency 角频率circular functions 圆函数circular helix 圆柱螺旋线circular measure 弧度circular motion 圆运动circular neighborhood 圆邻域circular orbit 圆轨道circular pendulum 圆摆circular permutation 循环排列circular ring 圆环circular section 圆截面circular sector 圆扇形circular segment 圆弓形circular slit domain 圆形裂纹域circular symmetry 圆对称circular transformation 圆变换circulation 循环circulation index 环粮数circulation of vector field 向量场的循环circulatory integral 围道积分circumcenter 外心circumcentre 外心circumcircle 外接圆circumcone 外切圆锥circumference 圆周circumscribe 外接circumscribed circle 外接圆circumscribed figure 外切形circumscribed polygon 外切多边形circumscribed quadrilateral 外切四边形circumscribed triangle 外切三角形circumsphere 外接球cissoid 蔓叶类曲线cissoidal curve 蔓叶类曲线cissoidal function 蔓叶类函数clairaut equation 克莱罗方程class 类class bound 组界class field 类域class field tower 类域塔class frequency 组频率class function 类函数class interval 组距class mean 组平均class number 类数class of conjugate elements 共轭元素类classical groups 典型群classical lie algebras 典型李代数classical mechanics 经典力学classical sentential calculus 经典语句演算classical set theory 经典集论classical statistical mechanics 经典统计力学classical theory of probability 经典概率论classification 分类classification statistic 分类统计classification theorem 分类定理classify 分类classifying map 分类映射classifying space 分类空间clear 擦去clifford group 克里福特群clifford number 克里福特数clockwise 顺时针的clockwise direction 顺时针方向clockwise rotation 顺时针旋转clopen set 闭开集closable linear operator 可闭线性算子closable operator 可闭算子closed ball 闭球closed circuit 闭合电路closed complex 闭复形closed convex curve 卵形线closed convex hull 闭凸包closed cover 闭覆盖closed curve 闭曲线closed disk 闭圆盘closed domain 闭域closed equivalence relation 闭等价关系closed extension 闭扩张closed filter 闭滤子closed form 闭型closed formula 闭公式closed geodesic 闭测地线closed graph 闭图closed graph theorem 闭图定理closed group 闭群closed half plane 闭半平面closed half space 闭半空间closed hull 闭包closed interval 闭区间closed kernel 闭核closed linear manifold 闭线性廖closed loop system 闭圈系closed manifold 闭廖closed map 闭映射closed neighborhood 闭邻域closed number plane 闭实数平面closed path 闭路closed range theorem 闭值域定理closed region 闭域closed riemann surface 闭黎曼面closed set 闭集closed shell 闭壳层closed simplex 闭单形closed solid sphere 闭实心球closed sphere 闭球closed star 闭星形closed subgroup 闭子群closed subroutine 闭型子程序closed surface 闭曲面closed symmetric extension 闭对称扩张closed system 闭系统closed term 闭项closeness 附近closure 闭包closure operation 闭包运算closure operator 闭包算子closure property 闭包性质clothoid 回旋曲线cluster point 聚点cluster sampling 分组抽样cluster set 聚值集coadjoint functor 余伴随函子coalgebra 上代数coalition 联合coanalytic set 上解析集coarser partition 较粗划分coaxial circles 共轴圆cobase 共基cobordant manifolds 配边廖cobordism 配边cobordism class 配边类cobordism group 配边群cobordism ring 配边环coboundary 上边缘coboundary homomorphism 上边缘同态coboundary operator 上边缘算子cocategory 上范畴cochain 上链cochain complex 上链复形cochain homotopy 上链同伦cochain map 上链映射cocircuit 上环道cocommutative 上交换的cocomplete category 上完全范畴cocycle 上闭键code 代吗coded decimal notation 二进制编的十进制记数法codenumerable set 余可数集coder 编器codiagonal morphism 余对角射codifferential 上微分codimension 余维数coding 编码coding theorem 编码定理coding theory 编码理论codomain 上域coefficient 系数coefficient domain 系数域coefficient function 系数函数coefficient functional 系数泛函coefficient group 系数群coefficient of alienation 不相关系数coefficient of association 相伴系数coefficient of covariation 共变系数coefficient of cubical expansion 体积膨胀系数coefficient of determination 可决系数coefficient of diffusion 扩散系数coefficient of excess 超出系数coefficient of friction 摩擦系数coefficient of nondetermination 不可决系数coefficient of rank correlation 等级相关系数coefficient of regression 回归系数coefficient of the expansion 展开系数coefficient of thermal expansion 热膨胀系数coefficient of variation 变差系数coefficient of viscosity 粘性系数coefficient problem 系数问题coefficient ring 系数环coercive operator 强制算子cofactor 代数余子式cofiber 上纤维cofibering 上纤维化cofibration 上纤维化cofilter 余滤子cofinal set 共尾集cofinal subset 共尾子集cofinality 共尾性cofinite subset 上有限子集cofunction 余函数cogenerator 上生成元cogredient automorphism 内自同构coherence 凝聚coherence condition 凝聚条件coherent module 凝聚摸coherent ring 凝聚环coherent set 凝聚集coherent sheaf 凝聚层coherent stack 凝聚层coherent topology 凝聚拓扑coherently oriented simplex 协同定向单形cohomological dimension 上同惮数cohomological invariant 上同祷变量cohomology 上同调cohomology algebra 上同碟数cohomology class 上同掂cohomology functor 上同弹子cohomology group 上同岛cohomology group with coefficients g 有系数g的上同岛cohomology module 上同担cohomology operation 上同邓算cohomology ring 上同捣cohomology sequence 上同凋列cohomology spectral sequence 上同底序列cohomology theory 上同帝cohomotopy 上同伦cohomotopy group 上同伦群coideal 上理想coimage 余象coincidence 一致coincidence number 叠合数coincidence point 叠合点coincident 重合的coinduced topology 余导出拓扑cokernel 上核collect 收集collectionwise normal space 成集体正规空间collective 集体collinear diagram 列线图collinear points 共线点collinear vectors 共线向量collinearity 共线性collineation 直射变换collineation group 直射群collineatory transformation 直射变换collocation method 配置法collocation of boundary 边界配置collocation point 配置点colocally small category 上局部小范畴cologarithm 余对数colorable 可着色的2006-6-5 11:16:00想知道您所在城市卖钢琴的琴行电话和地址吗？点击查看！风轻云淡头衔：副管理员等级：超级版主威望：9文章：5337积分：33083注册：2004年12月31日第 3 楼column 列column finite matrix 列有限矩阵column matrix 列阵column rank 列秩column space 列空间column vector 列向量combination 组合combination principle 结合原理combination with repetitions 有复组合combination without repetition 无复组合combinatorial analysis 组合分析combinatorial closure 组合闭包combinatorial dimension 组合维数combinatorial geometry 组合几何学combinatorial manifold 组合廖combinatorial method 组合方法combinatorial optimization problem 组合最优化问题combinatorial path 组合道路combinatorial problem 组合最优化问题combinatorial sphere 组合球面combinatorial sum 组合和combinatorial theory of probabilities 概率组合理论combinatorial topology 组合拓朴学combinatorially equivalent complex 组合等价复形combinatories 组合分析combinatory logic 组合逻辑combinatory topology 组合拓朴学combined matrix 组合矩阵comma 逗点command 命令commensurability 可通约性commensurable 可通约的commensurable quantities 可公度量common denominator 公分母common difference 公差common divisor 公约数common factor 公因子common factor theory 公因子论common fraction 普通分数common logarithm 常用对数common measure 公测度common multiple 公倍元common perpendicular 公有垂线common point 公共点common ratio 公比common tangent of two circles 二圆公切线communality 公因子方差communication channel 通讯通道commutant 换位commutation law 交换律commutation relation 交换关系commutative 可换的commutative diagram 交换图表commutative group 交换群commutative groupoid 阿贝耳广群commutative law 交换律commutative lie ring 交换李环commutative ordinal numbers 交换序数commutative ring 交换环commutativity 交换性commutator 换位子commutator group 换位子群commute 交换compact 紧的compact convergence 紧收敛compact group 紧群compact open topology 紧收敛拓扑compact operator 紧算子compact set 紧集compact space 紧空间compact subgroup 紧子群compact support 紧支柱compactification 紧化compactification theorem 紧化定理compactness 紧性compactness theorem 紧性定理compactum 紧统comparability of cardinals 基数的可比较性comparable curve 可比曲线comparable function 可比的函数comparable topology 可比拓扑comparable uniformity 可比一致性comparison function 比较函数comparison method 比较法comparison series 比较用级数comparison test 比较检验comparison theorem 比较定理compass 两脚规compatibile condition 相容性条件compatibility 一致性compatibility condition 相容性条件compatible system of algebraic equations 相容代数方程组compatible topology 相容拓扑学compensate 补偿compensating method 补偿法compensation 补偿compensation of error 误差的补偿compiler 编译程序compiling routine 编译程序complanar line 共面线complele induction 数学归纳法complement 补集complement of an angle 余角complementary 补的complementary angle 余角complementary degree 余次数complementary divisor 余因子complementary event 余事件complementary function 余函数complementary graph 余图complementary ideal 余理想complementary laws 补余律complementary module 补模complementary modulus 补模数complementary set 补集complementary space 补空间complementary submodules 补子模complementary subset 余子集complementary subspace 补子空间complemented lattice 有补格complete abelian variety 完备阿贝耳簇complete accumulation point 完全聚点complete axiom system 完备公理系统complete category 完全范畴complete class 完备类complete continuity 完全连续性complete disjunction 完全析取complete elliptic integral 完全椭圆积分complete field 完全域complete field of sets 集的完全域complete graph 完全图complete group 完全群complete group variety 完备群簇complete homomorphism 完全同态complete induction 数学归纳法complete integral 完全积分complete intersection 完全交叉complete lattice 完全格complete linear system 完备线性系统complete local ring 完全局部环complete measure 完全测度complete measure space 完备测度空间complete metric space 完备度量空间complete normality axiom 完全正规性公理complete ordered field 全序域complete orthogonal sequence 完全正交序列complete orthogonal set 完全正交系complete orthogonal system 完全正交系complete orthonormal sequence 完备标准正交序列complete orthonormal system 完备标准正交系complete probability space 完全概率空间complete quadrangle 完全四点形complete quadrilateral 完全四边形complete reducibility theorem 完全可约性定理complete regularity separation axiom 完全正则性分离公理complete reinhardt domain 完全赖因哈耳特域complete set 完全集complete solution 完全积分complete space 完备空间complete subcategory 完全子范畴complete system 完备系complete system of functions 函数完备系complete system of fundamental sequences 完全基本序列系complete system of invariants 完全的不变量系complete tensor product 完全张量积completed shell 闭壳层completely additive 完全加性的completely additive family of sets 完全加性集族completely additive measure 完全加性测度completely compact set 完全紧集completely continuous function 完全连续函数completely continuous linear operator 完全连续线性算子completely continuous mapping 全连续映射completely continuous operator 全连续映射completely distributive lattice 完全分配格completely homologous maps 完全同党射completely independent system of axioms 完全独立公理系统completely integrable 完全可积的completely integrable system 完全可积组completely integrally closed 完全整闭的completely mixed game 完全混合对策completely monotone 完全单的completely monotonic function 完全单弹数completely monotonic sequence 完全单凋列completely multiplicative 完全积性的completely multiplicative function 完全积性函数completely primary ring 完全准素环completely reducible 完全可约的completely reducible group 完全可约群completely regular filter 完全正则滤子completely regular space 完全正则空间completely regular topology 完全正则拓扑completely separated sets 完全可离集completely specified automaton 完全自动机。

金融随机分析(陈萍,南京理工大学)

(t ) r (t ) " noise "
Where we do not know the exact behaviour of the noise term, only its probability distribution. the function r(t)is assumed to be nonrandom. How do we solve (1.1)in this case?
3. Ak , Ak k 1
A pair (W, is called a measurable space. ) An element of is called a measurable subset of W • A s-algebra contains , so does W,
n
The integral of X, is defined as
W
X ( )dP() c P( F )
i 1 i i
15
n
3. X is nonnegative:
Xd : sup X d X ( ) X ( ) (Xn: simple function) lim X d 0 X ( ) X ( ) X ( )
0 1 2 k
(W, , {k }, P) is called a filtered space, where
0 1
8
1.2 Random variable,distribution
Definition 1.2.1: Given (W, , P), a function f : W is called measurable if

Measure-Theory

2
b} : −∞
a
b
+∞}
Check that C1 is an algebra. We call σ(C0 ) = σ(C1 ) the Borel σ-algebra of R. In general, C1 σ(C1 ). This means that the structure of σ(C1 ) is very complicated. Deﬁnition 1.11. Let (S, d) be a metric space. Let C be the total of all open sets. We call σ(C ) the Borel σ-algebra of (S, d), and denoted by B (S). E: Let C be the total of all open sets. Show that σ(C ) = σ(C ) = m(C ) = m(C ). 1.2. Measure and Extension. Deﬁnition 1.12. Let (Ω, F ) be a measurable space. Let µ : F → [0, ∞] be a set function. We call µ a measure on (Ω, F ) if µ(∅) = 0 and µ is countable additive, i.e., µ(∪An ) = µ(An ), An ∈ F are disjoint mutually.
1
(1.1)
பைடு நூலகம்
E: Let C be a σ-algebra. Let A ⊂ Ω. Show that A ∩ C := { A ∩ B : B ∈ C } is still a σ-algebra. Let C0 be a class of subsets of Ω. Let Γ be the class of all algebras that includes C0 . Denote by σ0 (C0 ) the class of sets in all algebras in Γ. Then σ0 (C0 ) is the smallest algebra containing C0 . Similarly, one can deﬁne the smallest σ-algebra σ(C0 ) containing C0 . We call σ(C0 ) the σ-algebra generated by C0 . Deﬁnition 1.6. (Monotone class of sets) A class C of subsets of Ω is a monotone class if C contains the limits of every monotone sequence. Similarly, for any C , there is a smallest monotone class m(C ) containing C . P: Like the completeness of real numbers, can m(C ) be obtained by adding some limit point of monotone sequence in C ? Theorem 1.7. (Monotone class theorem) Let C be an algebra. Then m(C ) = σ(C ). Proof. First of all, since σ(C ) is a class of monotone, we have m(C ) ⊂ σ(C ). On the other hand, if one can show that m(C ) is an algebra, then by the above exercise, m(C ) is a σ-algebra, and so σ(C ) ⊂ m(C ). To prove that m(C ) is an algebra. One needs to show m(C ) is closed under complementation and ﬁnite unions. The closedness of m(C ) under complementation is easy since the class of sets in m(C) whose complements are in m(C ) is a monotone class containing C (recalling that C is an algebra). Let us now prove the closedness of m(C ) under ﬁnite unions. Deﬁne C0 := {A ∈ m(C ) : A ∪ B ∈ m(C ), B ∈ C }, C1 := {A ∈ m(C ) : A ∪ B ∈ m(C ), B ∈ m(C )}. Clearly, C0 and C1 are monotone classes and C ⊂ C0 . Hence, C0 = m(C ) ⇒ C ⊂ C1 ⇒ C1 = m(C ). The proof is complete. Remark 1.8. The basic application of monotone class is that: Let P be a property and C an algebra. To verify that P holds for all A ∈ σ(C ), one can do as follows: Deﬁne C0 := {A ∈ σ(C ) : P holds for A}. If one can show that C ⊂ C0 and C0 is closed under monotone limits (a monotone class), then C0 = m(C ). There are other type monotone class theorem (See Yan’s book: Dykin’s class or λ-class). Example 1.9. Let Ω = {1, 2, · · · , 2n} and C = {{1}, {2}, · · · , {2n}}. It is easy to see that σ(C ) = 2Ω . But if C = {{2}, {4}, · · · , {2n}}, what is σ(C )? Example 1.10. Let C0 := {{ s ∈ R : a < s and C1 := A : A = ∪n i=1 Ai : Ai ∈ C0 , n ∈ N .

Cantor's Set Theory from a Modern Point of View

Cantor’s Set Theory from a Modern Point ofViewSy D.FriedmanSeptember27,2002Cantor earned his doctorate in Berlin in1867and was appointed in Halle in1869,where he soon after habilitated.Under the inﬂuence of Heine,his work moved to the study of trigonometric series,which led him necessarily into his investigations in set theory.In addition to developing his profound theory of transﬁnite numbers and cardinality,he showed that the algebraic numbers are countable(and therefore almost all reals are transcendental), the reals are not countable and n-dimensional Euclidean space can be put into1-1correspondence with the real line.He was appointed to a chair in Halle in1879.Cantor founded the DMV in1890and was elected itsﬁrst president the year after.Cantor’s ideas were revolutionary,and met signiﬁcant opposition,espe-cially from Kronecker.Mittag-Leﬄer persuaded Cantor to withdraw a paper that he had submitted to Acta Mathematica,on the grounds that he had submitted it“about100years too soon”!Fortunately Cantor also had the support of some important mathematicians,such as Dedekind.Cantor’s two key contributions were to provide us with theories of trans-ﬁnite counting and of inﬁnite cardinality.Transﬁnite counting arises naturally when one considers the Cantor deriva-tive:If C is a closed set of real numbers,then C′denotes the set of all limit points of C.Thus C⊇C′⊇C′′⊇···.Write C∞=C∩C′∩C′∩···.Then C∞⊇(C∞)′,and this inclusion may be strict.Thus one must keep counting past∞:C∞⊇C∞+1⊇C∞+2⊇···!The key feature of this new sequence of counting stages is that it forms1a wellordering,a linear ordering with no inﬁnite descending sequence of el-ements.Cantor showed that any two wellorderings are comparable in the sense that one is isomorphic to an initial segment of the other,and that the wellorderings can be canonically represented by special wellorderings where the ordering relation is given by the membership relation∈.Sets which carry such a special wellordering are called ordinals.Cantor’s view was that each well-deﬁned set carries a wellordering.Thus every set can be placed in1-1correspondence with an ordinal.But this ordinal is not unique.A cardinal is an ordinal which cannot be put into1-1 correspondence with a smaller ordinal.Then every set can be put into1-1 correspondence with a unique cardinal,called the cardinality of that set.Zermelo later justiﬁed Cantor’s view by proving that every set can indeed be wellordered,using the Axiom of Choice.Thus,Cantor’s theory does provide an excellent theory of cardinality for arbitrary sets.This theory left however one major gap:The Continuum Problem:What is the cardinality of the continuum?The Continuum Hypothesis(CH):Every uncountable set of reals has the same cardinality as the set of all reals.Cantor failed to solve this problem,and in fact it was later discovered that this problem cannot be solved using the currently accepted axioms for set theory.ParadoxesCantor,and independently Burali-Forti,found paradoxes in Cantor’s set theory.The most famous version of the paradox is due to Russell:If x consists of all sets y such that y/∈y,then x∈x↔x/∈x!Zermelo’s proposal was to avoid the paradoxes by conﬁning oneself to established principles of set-formation.He developed an axiomatic theory of sets,Zermelo set theory,which captures these principles and to the present day does appear to be free of contradiction.Fraenkel added a missing axiom scheme to Zermelo’s system,resulting in ZFC,Zermelo-Fraenkel set theory with the axiom of choice.This is the standard axiom system for set theory today.The Universe of Sets V2As a consequence of the ZFC axioms one has the following attractive picture of the set-theoretic universe V :V 0=∅¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡e e e e e e e e e e e e e e e e e e e e e e e e e e e e e V 2=P P (∅)...V ω+1=P (V ω)...V α+1=P (V α)...This provides the ﬁrst picture of the universe of sets,based on the ordinals and power set operation.But this is not a canonical description,in light of the vagueness of the power set operation.A consequence of this vagueness is that the continuum problem remains unsolved.The Vagueness of Power SetOne possible way to avoid the vagueness of power set is to focus on deﬁnable sets ,as did the descriptive set-theorists of the 1930s.A set of reals is Borel iﬀit belongs to the smallest σ-algebra containing all open sets.It is3Σ11(or analytic)iﬀit is the continuous image of a Borel set and isΠ11iﬀits complement isΣ11.Inductively,aΣ1n+1set is the continuous image of aΠ1n set and aΠ1n+1set is the complement of aΣ1n+1set.A set is projective iﬀit isΣ1n orΠ1n for some n.The descriptive set-theorists of the1930s were able to show thatΣ11sets do not violate the continuum hypothesis,in the sense that each uncountable Σ11set of reals does have the same cardinality as the reals.But they were unable to extend this toΠter work of G¨o del and Cohen implies that this indeed cannot be done in ZFC.Another approach to circumventing the vagueness of the power set oper-ation is due to G¨o del.Recall that in our picture of V,at a successor stage Vα+1one takes the all subsets of the previous stage Vα.G¨o del modiﬁed this hierarchy by instead taking only those subsets of the previous stage which can be produced using simple set-theoretic operations.He showed that itera-tion of this“weak”power set operation gives rise to a hierarchy of Lα’s whose union L is a model of ZFC.Moreover his hierarchy grows so slowly that sets are easily labelled by ordinal numbers,yielding the striking consequence that CH holds in L.This provided theﬁrst consistent interpretation of ZFC in which CH is demonstrably true.G¨o del himself did not consider L to be the correct interpretation of V, but only as a tool for showing that statements are consistent with the axioms of ZFC.This point of view is almost universal among set-theorists today. Indeed there are other consistent interpretations of the ZFC axioms.Cohen developed a technique for adding new sets to L while preserving the ZFC axioms.In fact,he was able to obtain such an interpretation where CH is false:A Cohen real over L is a real that belongs to every open dense set of reals which L can“describe”.By adding many Cohen reals to L,one obtains a consistent failure of CH.Cohen’s method,called forcing,is very general.Another of its applica-tions is the following:A real in[0,1]is random over L iﬀit belongs to every measure one subset of[0,1]which L can“describe”.Solovay[70]used this notion of forcing to obtain an interpretation of ZFC in which no projective set of reals violates the continuum hypothesis.Canonical UniversesThus we are faced with a dilemma:Must we accept diﬀerent universes4with diﬀerent kinds of mathematics;universes where CH holds and universes where it does not?This kind of undecidability is certainly very troubling,and has led set-theorists to search for a canonical,acceptable interpretation,or standard model,of ZFC which provides the“correct”answers to undecidable problems.G¨o del’s L is surely canonical,but rejected as being too restrictive, given the ease with which it can be modiﬁed by forcing.Unfortunately the universes constructed using forcing are not canonical:If there is one Cohen (random)real over L,then there are many.How does one obtain canonical universes which are larger than L?An answer came from measure theory.From work of Scott[61]and Solo-vay[71],we have:If there is a countably additive extension of Lebesgue measure to all sets of reals,then V is not L.And any model of ZFC with such a measure can be converted into a model of ZFC with a certain type of large cardinal number called a measurable cardinal(and vice-versa).Now Sil-ver[71]showed that if there is a measurable cardinal then there is a canonical subuniverse of V,or inner model,with a measurable cardinal.This provided theﬁrst canonical inner model larger than G¨o del’s L.Is Silver’s model the desired standard model of ZFC?To answer this question we consider the role of large cardinal hypotheses, of which the assumption of a measurable cardinal is an example.We say that two set-theoretic assertionsϕ,ψare consistency-equivalent iﬀone can show that ZFC+ϕhas a model iﬀZFC+ψhas a model.Experience shows that any natural set-theoretic assertionϕis consistency-equivalent to an assertionψ,whereψis either a large cardinal hypothesis or simply one of the statements0=0or0=1.Thus large cardinal hypotheses calibrate the strength of natural set-theoretic assertions.Hypotheses beyond the existence of a measurable cardinal are needed for this calibration.A nice example arises from descriptive set theory:A is Wadge reducible toB iﬀfor some continuous f,x∈A iﬀf(x)∈B. W P n:If A,B areΣ1n but notΠ1n then A is Wadge reducible to B and vice-versa.Now we haveW P1is consistency equivalent to the existence of#’s,a large cardinal axiom below a measurable cardinal(Martin[70]and Harrington[78]).5W P2is consistency-equivalent to(a little more than)the existence of a Woodin cardinal,a cardinal much larger than a measurable cardinal(Hjorth[96]). W P n seems to require at least n−1Woodin cardinals.Thus our desired standard model for ZFC should be big enough to permit the existence of Woodin cardinals.Silver’s model is therefore too small.The construction of canonical inner models for large cardinals at and above the level of Woodin cardinals is a central,ongoing project in pure set theory.These models however cannot be built using only the axioms of ZFC. Instead,one shows that if there is a large cardinal of a certain kind,then there is a canonical inner model with this kind of large cardinal.But isn’t this circular?Why should we allow these large cardinals at all?It is reasonableto assert that L is too restrictive,but need we assume that Woodin cardinals exist?Perhaps our position should be that W P n is simply false for n>1!The justiﬁcation of large cardinal hypotheses remains an important chal-lenge for pure set theory.One approach to this problem makes use of endo-morphisms.An inner model M is rigid iﬀthere is no1-1embedding M→M which preserves the basic set-theoretic operations union,product,diﬀerence, etc.The smallest large cardinal axiom,written“0#exists”,is equivalent to the statement that L is not rigid.If L is not rigid,there is a“canonical”inner model L#bigger than L which satisﬁes“L is not rigid”.Now do this again:If L#is not rigid then there is a canonical inner model L##where thisis true,etc.There is a canonical#operation which iterated in this way leadsto models with Woodin cardinals.This is analogous to G¨o del’s constructionof L,obtained through iteration of a weak power set operation.In G¨o del’s context,the axioms of ZFC justify the use of this operation.In the current context,one must argue for the non-rigidity of the models that arise in a canonical#-iteration.Such an argument can provide a justiﬁcation for the existence of inner models with Woodin cardinals.However no canonical#iteration is known which goes very far beyond Woodin cardinals.Luckily,most current applications of large cardinals do not use stronger hypotheses.Butﬁnding such an operation remains an im-portant problem if we wish to achieve a satisfying picture of the set-theoretic universe,a picture which would not only give rise to numerous further ap-plications of set theory and justify the use of large cardinal hypotheses,but also lend credence to the claim that the paradoxes that threatened Cantorin the infancy of set theory have been deﬁnitively resolved.6ReferencesL.Harrington[78]Analytic determinacy and0#,J.Symbolic Logic43(1978), no.4,pp.685–693.G.Hjorth[96]Π12Wadge degrees,Ann.Pure Appl.Logic77(1996),no.1, 53–74.D.Martin[70]Measurable cardinals and analytic games,Fund.Math.66, pp.287–291.D.Scott[61]Measurable cardinals and constructible sets,Bull.Acad.Polon. Sci.Ser.Sci.Math.Astronom.Phys.9(1961),pp.521–524.J.Silver[71]The consistency of the GCH with the existence of a measurable cardinal,in“Axiomatic Set Theory”(D.Scott,ed.),Proc.Sympos.Pure Math.,vol.XIII,Part1,Amer.Math.Soc.,1971,pp.391–395.R.Solovay[70]A model of set theory in which every set of reals is Lebesgue measurable,Ann.of Math.(2)92(1970),pp.1–56.R.Solovay[71]Real-valued measurable cardinals,in“Axiomatic Set Theory”(D.Scott,ed.),Proc.Sympos.Pure Math.,vol.XIII,Part1,Amer.Math. Soc.,1971,pp.397–428.7。

大学常见课程名称及英语翻译按字母排序及专业排序

大学各专业课程中英文对照A开头的课程ALGOL 语言ALGOL LanguageBASIC & FORTRAN 语言BASIC Language & FORTRAN LanguageBASIC 语言BASIC LanguageBASIC 语言及应用BASIC Language & ApplicationC 语言C LanguageC++ 程序设计C++ Program Desig ningCAD 概论Introduction to CADCAD/CAM CAD/CAMCET-4 College En glish T est (Ba nd 4)CET-6 College En glish T est (Ba nd 6)COBOL 语言COBOL LanguageCOBOL 语言程序设计COBOL Language Program DesigningC 与UNIX 环境C Language & Unix EnvironmentC 语言科学计算方法Scientific Computation Method in CC 语言与生物医学信息处理 C Lan guage & Biomedical In formation Process ing dBASE 川课程设计Course Exercise in dBASE 川FORTRAN 77 语言FORTRAN 77 LanguageFORTRAN 语言FORTRAN LanguageFoxBase 程序设计FoxBase ProgrammingHopf 代数Hopf AlgebraHopf 代数与代数群量子群Hopf Algebra , Algebraic Group and Qua ntum GroupIBM-PC/XT Fu ndame ntals of Microcomputer IBM-PC/XTIBM-PC 微机原理Fundamentals of Microcomputer IBM-PCProgrammi ng IBM 汇编及高级语言的接口IBM Assembly & its In terfaces with Adva needLanguagesInternet 与Intranet 技术Internet and Intranet Tech no logyLSI 设计基础Basic of LSI DesigningOS/2 操作系统OS/2 Operation SystemPASCAL 大型作业PASCAL Wide Range WorkingPASCAL 课程设计Course Exercise in PASCALPASCAL 语言PASCAL LanguagePC 机原理Principle of PCUnix 编程环境Unix Programming EnvironmentUnix 操作系统分析Analysis of Unix SystemVLSI 的EDA 技术EDA Techniques for VLSIVLSI 技术与检测方法VLSI Techniques & Its ExaminationVLSI 设计基础Basis of VLSI DesignWindows 系统Windows Operation SystemX 光分析X-ray AnalysisX 射线金属学X-Ray & MetallographyX 射线与电镜X-ray & Electric MicroscopeZ-80 汇编语言程序设计Z-80 Pragramming in Assembly LanguagesB开头的课程板壳非线性力学Non li near Mecha nics of Plate and Shell板壳理论Plate Theory , Theory of Plate and Shell板壳力学Plate Mecha nics办公自动化Office Automatizati on办公自动化系统毕业设计Office Automatizati on Thesis办公自动化系统设计Office Automatizatio n Desig n半波实验Semiwave Experime nt半导体变流技术Semic on ductor Converting Tech no logy半导体材料Semico nductor Materials半导体测量Measureme nt of Semic on ductors半导体瓷敏元件Semic on ductor Porcela in-Sen sitive Eleme nts半导体光电子学Semico nductor Optic Electro nics半导体化学Semic on ductor Chemistry半导体激光器Semico nductor Laser Un it半导体集成电路Semic on ductor In tegrated Circuitry半导体理论Semi-c on ductive Theory半导体器件Semic on ductor Devices半导体器件工艺原理Tech no logical Fun dame ntals of Semic on ductor Device 半导体器件课程设计Course Desig n of Semico nductor Devices半导体物理Semico nductor Physics半导体专业Semi-c onduction Specialty半导体专业实验Specialty Experime nt of Semic on ductor半群理论Semi-group Theory保健食品监督评价Evaluation and Supervisio n on Health Food s保险学In sura nee保险学In sura nee报告文学专题Special Subject On Reportage报刊编辑学Newspaper & Magazi ne Edit ing报干刊选读Selected Readi ngs of Newspaper & Magaz ine报纸编辑学Newspaper Edit ing泵与风机Pumps and Fans泵与水机Pumps & Water Turbi nes毕业论文Graduation Thesis毕业设计Graduatio n Thesis毕业实习Graduation Practice编译方法Compilatio n Method编译方法Methods of Compili ng编译技术Tech nique of Compil ing编译原理Fun dame ntals of Compili ng, Prin ciples of Compiler编译原理课程设计Course Design of Compi ling变电站的微机检测Computer Test ing in Tran sformer Substatio n变电站的微机检测与控制Computer Testi ng & Co ntrol in Tran sformer Substation变分法与量Calculus of Variati ons & Ten sor变分学Calculus of Variations变流技术Semic on ductor Converting Tech no logy变质量系统热力学与新型回转压Variable Quality System Thermal Mecha nics & NeoRo 表面活性剂化学及应用Chemistry and Applicatio n of Surfacta nt表面活性物质Surface Reactive Materials并行处理Parallel Processi ng并行处理与并行程序设计Parallel Process ing and Parallel Programmi ng并行算法Parallel Algorithmic波谱学Spectroscopy, Wave Spectrum波谱学实验Spectroscopic Experime nt薄膜光学Film Optics薄膜物理Thin Film Physics不育症的病因学Etiology of In fertilityC开头的课程材料的力学性能测试Measureme nt of Material Mecha nical Performa nee材料化学Material Chemistry材料力学Mecha nics of Materials财税法规与税务会计Laws and Regulati ons of Finance and T axes财务案例分析Case An alysis of Finance Man ageme nt财务案例分析Case An alysis of Finan cial Man ageme nt财务报告分析An alysis of Financial Stateme nt财务成本管理Fi nan cial Cost Man ageme nt财务管理Finan cial Man ageme nt, Finan cial Cost Man ageme nt财务会计Finan cial Acco untancy财政学Public Finance财政与金融Finance & Banking财政与税收Finance & Reven ue财政与税收理论Theories on Public Finance and T ax Reve nue财政与信贷Finance & Credit操作系统Disk Operati ng System (DOS)操作系统课程设计Course Desig n in Disk Operat ing System操作系统与编译原理Disk Operati ng System & Fun dame ntals of Compili ng操作系统原理Fun dame ntals of Disk Operati ng System, Prin ciples of Operati ng System 测量技术基础Foun datio n of Measureme nt Tech no logy测量原理与仪器设计Measureme nt Fun dame ntals & Meter Desig n测试技术Test ing Tech no logy测试与信号变换处理Test ing & Sig nal Tran sformati on Process ing策波测量技术Tech nique of Whip Wave Measureme nt策略管理Strategic Ma nageme nt产品学Production产业经济学In dustrial Economy产业组织In dustrial Organi zatio n财务管理与分析Finan cial Man ageme nt and An alysis 产业组织学In dustrial Organi zati on T ech no logy常微分方程Ordi nary Differe ntial Equatio ns场论Field Theory专业资料超导磁体及应用Superconductive Mag net & Application超导及应用Superc on ductive & Applicatio n超高真空科学与技术Scie nee and Techn ology of Ultrahigh Vacuum 60超精密加工和微细加工Super-Precision & Min ute ness Processi ng超精微细加工Super-Precision & Min ute ness Processi ng 超声及应用Supers onics Applicati on成本会计Cost Accou nting成像原理与技术Prin ciples & Tech nique of Imagi ng成组技术Group ing Tech nique城市规划原理Fun dame ntals of City Pla nning城市社会学Urban Sociology程控数字交换Program Con trolli ng of Digital Excha nge程序设计Program Desig ning程序设计方法学Methodology of Program ming. Methods of Program ming程序设计及算法语言Program Desig ning & Algorithmic Lan guage程序设计语言Program ming Lan guage齿轮啮合原理Prin ciples of Gear Co nn ecti on冲击测量及误差Pu nchi ng Measureme nt & Error冲压工艺Sheet Metal Formi ng Techn ology抽象代数Abstract Algebra初等数学Primary Mathematics传坳概论In troduction to Pass Col传动概论In troducti on to Tran smissi on传感技术Sen sor Tech nique传感技术及应用Sensor T echnique & Application传感器及应用Se nsors & Applicati on传感器与检测技术Se nsors & Testi ng Techn ology传感器原理Fun dame ntals of Sensors传感器原理及应用Fu ndame ntals of Sen sors & Application传热学Heat Tran sfer船舶操纵Ship Co ntrolli ng船舶电力系统Ship Electrical Power System船舶电力系统课程设计Course Exercise in Ship Electrical Power System 船舶电气传动自动化Ship Electrified Tran smissio n Automatio n船舶电站Ship Power Stati on船舶动力装置Ship Power Equipme nt船舶概论In troduction to Ships船舶焊接与材料Weldi ng & Materials on Ship船舶机械控制技术Mecha nic Con trol Tech nology for Ships船舶机械拖动Ship Mecha nic T owage船舶建筑美学Artistic Desig ning of Ships船舶结构Ship Structure船舶结构力学Structural Mecha nics for Ships船舶结构与制图Ship Structure & Graphi ng船舶静力学Ship Statics船舶强度与结构设计Desig ning Ship Inten sity & Structure船舶推进Ship Propelli ng船舶摇摆Ship Sway ing船舶摇摆与操纵Ship Swayi ng & Man ipulat ing船舶振动Ship Vibrati on船舶阻力Ship Resista nee船体建造工艺Ship-Buildi ng Techn ology船体结构Ship Structure船体结构图Ship Structure Graphi ng船体结构与制图Ship Structure & Graphi ng船体振动学Ship Vibratio n船体制图Ship Graph ing船用电器设备Mari ne Electrical Equipme nt创造心理学Creativity Psychology词汇学Lexicology磁测量技术Magn etic Measureme nt Tech no logy磁传感器Mag netic Sen sor磁存储设备设计原理Fun dame ntal Desig n of Magn etic Memory Equipme nt 磁记录Magn etographic磁记录技术Magn etographic T ech no logy磁记录物理Magn etographic Physics磁路设计与场计算Mag netic Path Desig ning & Mag netic Field Calculati磁盘控制器Mag netic Disk Con troler磁性材料Mag netic Materials磁性测量Mag netic Measureme nt磁性物理Mag netophysics磁原理及应用Prin ciples of Catalyzation & Application催化原理Prin ciples of CatalysisD开头的课程大电流测量Super-Curre nt Measureme nt大电源测量Super-Power Measureme nt大机组协调控制Coordi nation & Con trol of Gen erator Networks大跨度房屋结构Large-Spa n House structure大型锅炉概况In troduction to Large-Volume Boilers大型火电机组控制Control of Large Thermal Power Gen erator Networks大型数据库原理与高级开发技术Prin ciples of Large-Scale Data-Bas e and Adva need Developme ntTech no logy大学德语College Germa n大学俄语College Russia n大学法语College French大学日语College Japa nese大学生心理学Psychology In troduction大学物理College Physics大学物理实验Experime nt of College Physics大学英语College En glish大学语文College Chi nese大众传播学Mass Media代数几何Algebraic Geometry代数几何Algebraic Geometry代数曲面Algebraic Surfaces代数图论Algebraic Graph Theory代数拓扌卜Algebraic T opology代数学Algebra代用燃料Substitute Fuel代用运放电路Simulated Tran smittal Circuit单片机与接口技术Mon o-Chip Computers & In terface Tech ni que单片机原理Fu ndame ntals of Mon o-Chip Computers单片机原理及应用Fun dame ntals of Mo no-Chip Computers & Applicatio ns 弹塑性力学Elastic-Plastic Mecha nics弹性波Elastic Waves弹性力学Elastic Mecha ni cs, Theory of Elastic Mecha nics弹性元件的理论及设计Theory and Desig n of Elastic Eleme nt蛋白质结构基础Prin ciple of Protein Structure蛋白质生物化学技术Biochemical T echnology of Protein当代国际关系Con temporary Intern ati onal Relati on ship当代国外社会思维评价Evaluation of Con temporary Foreign Social Thought 当代文学Con temporary Literature当代文学专题Topics on Con temporary Literature当代西方哲学Con temporary Western Philosophy当代戏剧与电影Con temporary Drama & Films当代资本主义经济Con temporary Capitalist Economy党史History of the Party导波光学Wave Guidi ng Optics德育Moral Education等离子体工程Plasma Engin eeri ng低频电子线路Low Freque ncy Electric Circuit低温测试技术Cryo Testi ng Techni que低温传热学Cryo Co nduction低温固体物理Cryo Solid Physics低温技术原理与装置Fun dame ntals of Cryo Tech no logy & Equipme nt 低温技术中的微机原理Priciples of Microcomputer in Cryo Techn ology 低温绝热Cryo Heat In sulation低温气体制冷机Cryo Gas Refrigerator低温热管Cryo Heat Tube彳氐温设备Cryo Equipme nt低温生物冻干技术Biological Cryo Freez ing Drying Tech no logy低温生物学原理与应用Prin ciple & Applicatio n of Cryobiology低温实验技术Cryo Experime ntatio n Tech no logy低温物理导论Cryo Physic Co ncepts低温物理概论Cryo Physic Co ncepts低温仪表及测试Cryo Meters & Measureme nt低温原理Cryo Fun dame ntals低温原理与设备Cryo Fun dame ntals & Equipme nt低温制冷机Cryo Refrigerator低温中的微机应用Applicatio n of Microcomputer in Cryo Tech nology低温装置Cryo Equipme nt低噪声电子电路Low-Noise Electric Circuit低噪声电子设计Low-Noise Electro nic Desig ning低噪声放大与弱检Low-Noise In creas ing & Decreas ing低噪声与弱信号检测Detect ion of Low Noise & Weak Sign als地基基础课程设计Course Desig n of Groun dsill Basis地理Geography第二次世界大战史History of World War II典型计算机分析Classical Computer An alysis 电测量技术Electric Measureme nt Tech no logy 电厂计算机控制系统Computer Con trol System in Power Plants电磁测量实验技术Electromag netic Measureme nt Experime nt & Tech no logy电磁场计算机Electromag netic Field Computers电磁场理论Theory of Electromag netic Fields电磁场数值计算Numerical Calculatio n of Electromag netic Fields电磁场与电磁波Electromag netic Fields & Mag netic Waves电磁场与微波技术Electromag netic Fields & Micro-Wave Techn ology电磁场中的数值方法Numerical Methods in Electromag netic Fields电磁场中的数值计算Numerical Calculati on in Electromag netic Fields电磁学Electromag netics电动力学Electrody namics电镀Plating电分析化学Electro-A nalytical Chemistry电工材料Electrical Materials电工测量技术基础Measureme nt Tech no logy of Electrical Engin eeri ng 电工测试技术基础Testi ng Tech no logy of Electrical Engin eeri ng电工产品学Electrotech ni cal Products电工电子技术基础Electrical T ech no logy & Electrical Engin eeri ng电工电子学Electro nics in Electrical Engin eeri ng电工基础Fun dame ntal Theory of Electrical Engin eeri ng电工基础理论Fun dame ntal Theory of Electrical Engin eeri ng电工基础实验Basic Experime nt in Electrical Engin eeri ng电工技术Electrotech nics电工技术基础Fun dame ntals of Electrotech nics电工实习Electrical Engin eeri ng Practice电工实验Experime nt of Electrical Engin eeri ng电工实验技术基础Experime nt Tech no logy of Electrical Engin eeri ng 电工学Electrical Engin eeri ng电工与电机控制Electrical En gi neeri ng & Motor Con trol电弧电接触Electrical Arc Con tact电弧焊及电渣焊Electric Arc Weldi ng & Electroslag Weldi ng电化学测试技术Electrochemical Measureme nt T ech no logy电化学工程Electrochemical Engin eeri ng电化学工艺学Electrochemical T ech no logy电机Motor电机测试技术Motor Measuri ng Techn ology电机电磁场的分析与计算An alysis & Calculatio n of Electrical Motor &电机电磁场的数值计算Calculatio n of Electrical Motor & Electromag netic Fields 电机电磁场理论Theory of Electrical Moto & Electromag netic Fields电机电器与供电Motor Eleme nts and Power Supply电机矩阵分析法An alysis of Electrical Motor Matrix电机课程设计Course Exercise in Electric Engine电机绕组理论Theory of Motor Win di ng电机绕组理论及应用Theory & Applicati on of Motor Win di ng电机设计Desig n of Electrical Motor电机瞬变过程Electrical Motor Cha nge Processes电机统一理论Theory of Electrical Motor In tegration电机学Electrical Motor电机学及控制电机Electrical Mach in ery Con trol & Tech nology电机与拖动Electrical Machi nery & Towage电机原理Prin ciple of Electric Engine电机原理与拖动Prin ciples of Electrical Machi nery & Towage电机专题Lectures on Electric Engine电接触与电弧Electrical Co ntact & Electrical Arc电介质物理Dielectric Physics电镜Electronic Speculum电力电子电路Power Electr onic Circuit电力电子电器Power Electro nic Equipme nt电力电子器件Power Electro nic Devices电力电子学Power Electro nics电力工程Electrical Power Engin eeri ng电力企业管理Man ageme nt of Electrical En terprise电力生产技术Tech no logy of Electrical Power Gen erati on电力生产优化管理Optimal Ma nageme nt of Electrical Power Ge neration电力拖动Electric Tracti on电力拖动基础Fun dame ntals for Electrical Towage电力拖动控制系统Electrical T owage Control Systems电力拖动与电气控制Electrical T owage & Electrical Control电力系统Power Systems电力系统电源最优化规划Optimal Pla nning of Power Source in a Power System 电力系统短路Power System Shortcuts电力系统分析Power System An alysis电力系统规划Power System Pla nning电力系统过电压Hyper-Voltage of Power Systems电力系统继电保护原理Power System Relay Protecti on电力系统经济分析Econo mical An alysis of Power Systems电力系统经济运行Econo mical Operati on of Power Systems电力系统可靠性Power System Reliability电力系统可靠性分析Power System Reliability An alysis电力系统课程设计Course Desig n of Power Systems电力系统无功补偿及应用Non-Work Compe nsation in Power Systems & Applicati 电力系统谐波Harmonious Waves in Power Systems电力系统优化设计Optimal Desig ning of Power Systems电力系统远动Operati on of Electric Systems电力系统远动技术Operation Tech nique of Electric Systems电力系统运行Operati on of Electric Systems电力系统自动化Automation of Electric Systems电力系统自动装置Power System Automation Equipme nt电力系统最优规划Optimal Pla nning in Power System电力装置课程设计Course Desig n of Power Equipme nt电力装置与系统Power Equipme nt & System电路测量与实验Circuit Measureme nt & Experime nt电路测试技术Circuit Measureme nt Techn ology电路测试技术基础Fun dame ntals of Circuit Measureme nt Tech no logy电路测试技术及实验Circuit Measureme nt Techno logy & Experime nts电路分析基础Basis of Circuit An alysis电路分析基础实验Basic Experime nt on Circuit An alysis电路分析实验Experime nt on Circuit An alysis电路和电子技术Circuit and Electro nic T echni que电路基本理论Basis Theory of Circuitry电力系统可靠性分析Power System Reliability An alysis 电路及电子线路CAD Circuitry CAD电路理论Theory of Circuit电路理论基础Fun dame ntal Theory of Circuit电路理论实验Experime nts in Theory of Circuct电路设计与测试技术Circuit Desig ning & Measureme nt Techn ology电气测量技术Electrical Measureme nt Techn ology电气传动Electrified Tran smissi on电气控制技术Electrical Co ntrol Techn ology电器设计Electrical Applia nces Desig ning电器学Electrical Applia nces电器与控制Electrical Applia nces & Co ntrol电生理技术基础Basics of Electricphysiological T ech no logy电视传感器图象显示Televisi on Sen sor Graphic Display电视接收技术Televisi on Recepti on T ech no logy电视节目Televisi on Programs电视节目制作Televisi on Program Desig ning电视新技术New Televisio n T ech no logy电视新闻Televisio n News电视原理Prin ciples of Televisio n电网调度自动化Automation of Electric Network Ma nageme nt电学实验Electrical Experime nt电影艺术Art of Film Maki ng电站微机检测控制Computerized Measureme nt & Con trol of Power Statio电子材料与元件测试技术Measuri ng Techno logy of Electro nic Material and Eleme nt电子材料元件测量Electro nic Material and Eleme nt Measureme nt电子测量与实验技术Tech no logy of Electr onic Measureme nt & Experime nt电子测试Electronic T esting电子测试技术Electr onic Testi ng Tech no logy电子测试技术与实验Electr onic T esti ng Tech no logy & Experime nt电子测试实验Electr onic Test ing Experime nt电子测试与实验技术Electr onic T esti ng Tech no logy & Experime nt电子机械运动控制技术Techno logy of Electro nic Mecha nic Moveme nt Co ntrol电子技术Tech no logy of Electr onics电子技术腐蚀测试中的应用Application of Electro nic Techno logy in Erosion Measureme nt 电子技术基础Basic Electr onic T ech no logy电子技术基础与实验Basic Electr onic T ech no logy & Experime nt电子技术课程设计Course Exercise in Electro nic T ech no logy电子技术实验Experime nt in Electr onic T ech no logy电子技术综合性设计实验Experime nt in Electro nic Techn ology电子理论实验Experime nt in Electro nic Theory电子商务Electro nic Commerce电子系统的ASIC 技术ASIC Design T echnologies电子显微分析Electro nic Micro-A nalysis电子显微镜Electro nic Microscope电子线路Electro nic Circuit电子线路的计算机辅助设计Computer Associate Desig n of Electro nic Circuit电子线路课程设计Course Desig n of Electro nic Circuit电子线路设计与测试技术Electro nic Circuit Desig n & Measureme nt Techno logy 电子线路设计与测试实验Electro nic Circuit Desig n & Measureme nt Experime nt 电子线路实验Experime nt in Electro nic Circuit电子学Electr onics电子学课程设计Course Desig n of Electr onics电子照相技术Electr onic Photograph ing Tech no logy雕塑艺术欣赏Appreciation of Sculptural Art调节原理Prin ciples of Regulatio n调节装置Regulati on Equipme nt动力机械CAD Dynamical Machine CAD动力学Dyn amics动态规戈U Dyn amic Program ming动态无损检测Dyn amic Non-Destruction Measureme nt动态信号Dyn amic Sig nal动态信号分析与仪器Dy namic Sig nal An alysis & Apparatus动物病害学基础Basis of Ani mal Disease动物免疫学Ani mal Immu nology动物生理与分子生物学Ani mal Physiology and Molecular Biochemistry动物学Zoology动物遗传工程An imal Gen etic En gi neeri ng毒理遗传学Toxicological Gen etics断裂力学Fracture Mecha nics断裂疲劳力学Fatigue Fracture Mecha nics锻压测试技术Forging Test ing Tech nique锻压工艺Forging Tech no logy锻压机械液压传动Hydraulic Tran smissi on in Forging Mach inery 锻压加热设备Forging Heat ing Equipme nt锻压设备专题Lectures on Forging Press Equipme nts锻压系统动力学Dyn amics of Forgi ng System锻造工艺Forging Tech no logy锻造加热设备Forging Heat Equipme nt对外贸易保险Intern ati onal Trade In sura nee对外贸易地理Intern ati onal Market ing Geography对外贸易概论In troduct ion to Intern ati onal Trade对外贸易运输International Trade Transportation多层网络方法Multi-Layer Network Tech no logy多复变函数An alytic Fun ctio ns of Several Complex Variables多媒体计算机技术Multimedia Computer Techno logy多媒体技术Multimedia Techn ology多目标优化方法Multipurpose Optimal Method多项距阵Multi-Nomi nal Matrix多元统计分析Multivariable StatisticsF开头的课程发电厂Power Pla nt发电厂电气部分与动力部分Electric Eleme nts & Dyn amics of Power Pla nts发电厂电气部分与热力设备Electric Eleme nts & Thermody namics Equipme nt of Power Pla nts 发电厂计算机控制Computer Control in Power Pla nt发酵工程Zymolysis Engin eeri ng发育生物学原理与实验技术Prin ciple and Experime ntal Techno logy of Developme nt发展经济学Evolutive Econ omics法理学Nomology法律基础Fun dame ntals of Law法学概论An In troduct ion to Science of Law法学基础Fun dame ntals of Science of Law翻译Translation翻译理论与技巧Theory & Skills of Tra nslatio n反不正当经济法An ti-malfeasa nee Econo mic Law泛读Extensive Reading泛函分析Fun cti onal An alysis泛函分析Fun cti onal An alysis房屋建筑学Architectural Desig n & Con structio n房屋建筑学课程设计Course Desig n of House Architecture仿真与辅助设计Simulation & Computer Aided Desig n放射生物学Radiatio n Biology放射学Radiology非电量测量Non-Electricity Measureme nt非金属材料Non-Metal Materials非线性采样系统No n-Li near Sampli ng System非线性方程组的数值解法Numerical Methods for No-li near System s of Equati ons非线性光学Non li near Optics非线性规划No n-Lin ear Programmi ng非线性控制理论Non-Lin ear Con trol TheoryHyperbolic 非线性双曲型守恒律解的存在性The Existenee of Solutions for Non -linearCon servatio n Laws非线性物理导论In troduction to Non li near Physics非线性振荡Non-Linear Oscillation非线性振动Nonlinear Vibratio n废水处理工程Tech no logy of Wastewater Treatme nt废水处理与回用Sewage Disposal and Re-use沸腾燃烧Boili ng Combustio n分布式计算机系统Distributed Computer System / Distributed System分布式系统与分布式处理Distributed Systems and Distributed Process ing分离科学Separati on Science分析化学An alytical Chemistry分析化学实验An alytical Chemistry Experime nt分析力学An alytic Mecha nics分析生物化学An alytical Biochemistry分析生物化学An alytical Biochemistry分子病毒学Molecular Virology分子生物学Molecular Biology分子生物学技术Protocols in Molecular Biology分子遗传学Molecular Gen etics风机调节Fan Regulation风机调节使用.运转Regulatio n, Applicatio n & Operatio n of Fa ns风机三元流动理论与设计Tri-Varia nt Moveme nt Theory & Desig n of Fa ns风能利用Wind Power Utilizatio n风险投资分析An alysis of Risk In vestme nt服务业营销Service In dustry Marketi ng辅助机械Aided Machi ne腐蚀电化学实验Experime nt in Erosive Electrochemistry复变函数Complex Variables Functions复变函数与积分变换Functions of Complex Variables & In tegral Tran sformati on 复合材料结构力学Structural Mecha nics of Composite Material复合材料力学Compou nd Material Mecha nics傅里叶光学Fourier OpticsG开头的课程概率论Probability Theory概率论与数理统计Probability Theory & Mathematical Statistics概率论与随机过程Probability Theory & Stochastic Process概率与统计Probability & Statistics钢笔画Pen Drawi ng钢的热处理Heat-Treatme nt of Steel钢结构Steel Structure钢筋混凝土Rei nforced Con crete钢筋混凝土及砖石结构Reinforced Con crete & Brick Structure钢砼结构Re in forced Concrete Structure钢砼结构与砌体结构Re in forces Structure and Mo nsary Structure 钢砼课程设计Rein forced Con crete Course Desig n钢砼设计Experime nt of Rei nforced Con crete Structure高层建筑基础Tall Buildi ng Fou ndatio n高层建筑基础设计Desig ning bases of High Rising Buildi ngs高层建筑结构设计Desig ning Structures of High Risi ng Buildi ngs 高等材料力学Adva need Material Mecha nics高等代数Adva need Algebra高等发光分析Adva need Lumin esce nee An alysis高等分析化学Adva need An alytical Chemistry高等工程力学Adva need Engin eeri ng Mecha nics高等光学Adva need Optics高等环境微生物Adva need Environmen tal Microorga nism高等教育管理Higher Educatio n Man ageme nt高等教育史History of Higher Education高等教育学Higher Educatio n高等量子力学Adva need Qua ntum Mecha nics高等生物化学Adva need Biochemistry高等数理方法Adva need Mathematical Method高等数学Adva need Mathematics高等数值分析Adva need Numeric An alysis高等土力学Advanced Soil Mecha nics高等无机化学Adva need Inorganic Chemistry高等有机化学Adva need Orga nic Chemistry高电压测试技术High-Voltage Test Techn ology高电压技术High-Voltage Techn ology高电压技术与设备High-Voltage Tech no logy and Device高电压绝缘High-Voltage In sulation高电压实验High-Voltage Experime nt高分子材料High Polymer Material高分子材料及加工High Polymer Material & Porcessi ng高分子化学High Polymer Chemistry高分子化学实验High Polymer Chemistry Experime nt高分子化学与物理Polymeric Chemistry and Physics高分子物理High Polymer Physics高分子物理实验High Polymer Physics Experime nt高级程序设计语言的设计与实现Adva need Program ming Lan guage's Desig n & Impleme ntati on 高级管理信息系统Adva need Man ageme nt In formati on Systems高级计算机体系结构Adva need Computer Architecture高级计算机网络Adva need Computer Networks高级计算机网络与集成技术Adva need Computer Networks and In tegratio n T ech no logy 高级经济计量Adva need Econo mic Metrology高级软件工程Adva need Software Engin eeri ng咼级生化技术Adva need Biochemical T ech nique高级生物化学Adva need Biochemistry高级食品化学Adva need Food Chemistry高级视听Adva need Videos高级数据库Advanced Database高级数理逻辑Adva need Numerical Logic高级水生生物学Adva need Aquatic Biology高级英语听说Adva need En glish Liste ning & Speak ing高级植物生理生化Adva need Pla nt Physiology and Biochemistry高能密束焊High En ergy-De nse Beam Weldi ng高频电路High-Freque ncy Circuit咼频电子技术High-Freque ncy Eleetr onic T ech no logy高频电子线路High-Freque ncy Electro nic Circuit高维代数簇Algebraic Varieties of Higher Dime nsio n咼压测量技术High-Voltage Measureme nt Tech no logy咼压测试技术High-Voltage Test ing Tech no logy高压电场的数值计算Numerical Calculati on in High-Voltage Electro nic Field高压电工程High-Voltage Engin eeri ng高压电技术High-Voltage Techn ology高压电器High-Voltage Electrical Applia nces高压绝缘High-Voltage In sulation高压实验High-Voltage Experime ntati on高压实验设备测量High-Voltage Experime ntati on Equipme nt Measureme nt 高压试验技术High-Voltage Experime ntati on Tech no logy工厂电气设备Electric Equipme nt of Pla nts工厂供电Factory Electricity Supply工程材料的力学性能测试Mechanic T esting of Engineering Materials工程材料及热处理Engin eeri ng Material and Heat Treatme nt工程材料学Engin eeri ng Materials工程测量Engin eeri ng Surveying工程测量实习Engin eeri ng Measuri ng Practice工程测试技术Engin eeri ng Test ing Tech nique工程测试实验Experime nt on Engin eeri ng Testi ng工程测试信息In formati on of Engin eeri ng Test ing工程测试与信号处理Engin eeri ng Testi ng & Signal Process ing工程地质Engin eeri ng Geology工程动力学Engin eeri ng Dyn amics工程概论In troducti on to Engin eeri ng工程概预算Project Budget工程经济学Engin eeri ng Econo mics工程静力学Engin eeri ng Statics工程力学Engin eeri ng Mecha nics工程热力学Engin eeri ng Thermod yn amics工程数学Engin eeri ng Mathematics工程项目概预算Engin eeri ng Project Estimate & Budget工程项目评估Engin eeri ng Project Evaluati on工程优化方法Engin eeri ng Optimizati on Method工程运动学Engin eeri ng Kin ematics工程造价管理Engin eeri ng Cost Man ageme nt工程制图Graphi ng of Engin eeri ng工业产品学In dustrial Products工业电子学In dustry Electr on ics工业分析In dustrial An alysis工业锅炉In dustrial Boiler工业会计学In dustrial Acco unting工业机器人In dustrial Robot工业技术基础Basic In dustrial Tech nology工业技术经济In dustrial Tech no logy Economics工业建筑设计原理Prin ciples of In dustrial Buildi ng Desig n工业经济理论In dustrial Econo mic Theory工业经济学In dustrial Economics工业美术设计Art Desig ning in In dustry工业企业财务管理In dustrial En terprise Finan cial Man ageme nt工业企业财务会计Acco un ti ng in In dustrial En terprises工业企业管理In dustrial En terprise Man ageme nt工业企业经营管理In dustrial En terprise Admi nistrative Man ageme nt工业社会学In dustrial Sociology工业心理学In dustrial Psychology工业窑炉In dustrial Stoves工艺过程自动化Tech nics Process Automati on工艺设计Tech nics Desig n工艺实习Tech nics Practice工艺原理与研究方法Prin ciples & Research of Tech nics公差Com mon Differenee公差测试实验Com mon Differe nee Test ing Experime nt公差技术测量Tech ni cal Measureme nt with Common Difference公差与配合Com mon Differenee & Cooperation公共关系Public Relatio nship公共关系学Public Relatio ns公司法Corporati on Law公司组织与管理Organi zati on and Man ageme nt公司组织与管理Organi zati on and Man ageme nt of Corporate公文写作Docume nt Writi ng功能材料原理与技术Prin ciple and Tech no logy of Fu nctio nal Materials 功能高分子Fu nctio nal Polymer功能性食品Fu nction Foods古代汉语Ancient Chi nese古典文学作品选读Selected Readi ngs in Classical Literature骨科医学Osteopathic Medici ne固体磁性理论Theory of Mag netism in Solid固体激光Solid State Laser固体激光器件Solid Laser Eleme nts固体激光与电源Solid State Laser & Power Un it固体理论Solid State Theory固体物理Solid-State Physics故障诊断与容错技术Malfu nction Diag noses & Tolera nee Techno logy 关税Tariff管理概论In troducti on to Man ageme nt管理沟通Man ageme nt Com mun icatio n, Man ageme nt Negotiati on管理会计Man agerial Acco un ti ng管理经济学Man ageme nt Economics管理科学专题Man ageme nt Science Special Subject管理数学Ma nageme nt Mathematics管理系统FOXBASE Management System of FOXBASE管理系统模拟Man ageme nt System Simulation管理心理学Ma nageme nt Psychology管理信息系统Man ageme nt In formatio n System管理学Man ageme nt Theory, Prin ciples of Man ageme nt管理学Prin ciples of Man ageme nt光波导理论Light Wave Guide Theory光电技术Photoelectric T ech no logy光电检测与信号处理Optoelectro nic Detection and Process ing。

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目的论与戏剧翻译 _ 浅析莎士比亚名剧Measure for Measure的三个中文译本

目的论与戏剧翻译 _ 浅析莎士比亚名剧Measure forMeasure的三个中文译本提要众所周知,戏剧作为一种特殊的文学体裁,还同时具有舞台表演的特性,这导致了戏剧翻译中的一对矛盾:是将源文本的文化特征淋漓尽致地表达出来,还是为舞台表演牺牲部分文化因素?研究并解决这一矛盾成为当前戏剧翻译研究的重中之重。

而纵观中外翻译史,翻译界对戏剧翻译所作的研究为数并不多,且缺乏系统的理论指导,对戏剧中这一矛盾的关注更是不够。

本文尝试从目的论出发来审视这一矛盾,以目的论为研究的理论框架,试图证明目的论对研究和解决戏剧翻译中的矛盾行之有效,在戏剧翻译中意义重大。

作为文学艺术和舞台艺术的结合体,戏剧具有双重性。

这种双重性使得传统翻译理论难以指导或评估戏剧翻译。

而目的论主张翻译目的为翻译活动中的首要决定因素,这为翻译研究,特别是戏剧翻译研究开拓了新的视野。

只要译文实现了既定翻译目的,那么该译本就算是成功的译本。

为验证目的论在戏剧翻译中的可行性,本文运用该理论评价莎士比亚“Measure for Measure”的三个中文译本,以期从成功的翻译实践中找到有益启示。

全文由五个章节构成。

第一章对戏剧进行全面介绍,总结戏剧语言的特性,进一步指出戏剧翻译中的矛盾,并回顾了翻译界的相关研究。

第二章引进目的论的理论框架,阐明其主要概念及其对戏剧翻译的特殊意义。

第三章从目的论影响译者翻译方法的四个因素出发,介绍原作者莎士比亚、译者梁实秋、朱生豪和英若诚的相关信息。

第四章从目的论的角度,对三个译本进行了详尽分析,进一步验证目的论在戏剧翻译中的可行性。

第五章总结目的论在戏剧翻译中的重要意义及深远影响。

关键词:戏剧翻译,目的论,文学性,舞台表演 ivTABLE OF CONTENTSChapter I General Introduction to Drama and Drama Translation. 11.1 Definition of Drama: Literary Art & Theatrical Art11.2 Features of Dramatic Language: Speakability & Individuality.21.3 Duality of Drama Translation: Performance-oriented & Reader-oriented..31.4 Relevant Study of Drama Translation51.4.1 Drama Translation Theories in China..51.4.2 Drama Translation Theories in Western Countries7Chapter II The Skopos Theory and Drama Translation. 112.1 Development of the Skopos Theory. 112.2 Two Rules of the Skopos Theory122.3 Five Points of the Skopos Theory..132.4 Factors Affecting Translators’ Strategies from the Skopos Theory’s Standpoint..142.5 Significance of the Skopos theory for Drama Translation.15Chapter III Researches on Three Chinese Shakespearean translators from the Skopos Theory’sStandpoint..173.1 William Shakespeare and his Measure for Measure.173.2 Liang Shiqiu and his Complete Works of Shakespeare183.2.1 Initiator or Commissioner183.2.2 Translator.193.2.3 Source-text Producer and Target-text Receiver213.3 Zhu Shenghao and his Translation of Shakespeare..223.3.1 Initiator or Commissioner223.3.2 Translator.233.3.3 Source-text Producer, Target-text Receiver243.4 Ying Ruocheng and his Drama Translation..243.4.1 Initiator and Translator.243.4.2 Source-text Producer and Target-text Receiver26Chapter IV Sample Analysis274.1 Characters’ Names.274.2 Allusions.284.3 Metaphors..314.4 Idioms..344.5 Puns..374.6 Obscene Words404.7 Summary42Chapter V Conclusion 44BIBLIOGRAPHY 46vChapter I General Introduction to Drama and Drama TranslationDrama translation is a special and distinctive branch of literary translation due to thedualistic nature of drama. Then what on earth are the unique features of drama and dramatranslation? We may start our discussion with a general introduction to drama and relevantstudy of drama translation before going any further1.1 Definition of Drama: Literary Art & Theatrical ArtOriginally, the wor d “Drama” comes from a Greek word, “dran”, meaning “thingdone”, “action” or “deed”. To make it clear, the author looks up the word “drama” inseveral authoritative dictionaries and collects the following interpretations for furtherreference:ndIn the Oxford English Dictionary 2 Edition 1989, “Drama” is “a composition inprose or verse, adapted to be acted upon a stage, in which a story is related by means ofdialogue and action, and is represented with accompanying gesture, costume, and scenery,as in real life; a play”In the Encyclopedia Britannica 1964: “Drama” is “a form of art in which the artistimagines a story concerning persons and incidents without himself describing, narrating orexplaining what is happening”In the Encyclopedia Americana 1986: “Drama” is “a form of literature intended forperformance by actors. In general the subject matter is narrative in character and, in thetype of story traditionally considered suitable for presentation onthe stage”We may summarize the above interpretations like this: drama is a genre of literaturewith a story related by means of dialogue and action, and produced to be acted upon thestage. The term “drama” is used in an inclusive way that emphasizes both its literary natureon page for the reader and its potential for performance on stage for the audience. On theone hand, it is literature whose aesthetic effect depends on a collective endeavor and thereceptor’s response is mostly spontaneous and immediate. Since the play text containsstage directions and dramatic language which depict the portraits of characters and pushforward the plot, we can still read the play text as any other literary works. On the other1hand, drama is “an audiovisual presentation of time and space, involving music, dance,fine arts and literary language, with the simultaneous presence of actors and audience” Lin,1993: 4. The original intention and full potential of drama can only be brought out andrealized by performing on stage. Thus the ultimate receptor of drama is supposed to be theaudience in the theatreAlthough most dramas are produced to be performed, there is an exception. Somedramatic works are called “closet dramas” or “closet plays”, which are created to be readIn this case the playwright does not need to take theatrical performance into considerationHowever, plays with such a pure purpose are scarce, and here in this thesis, we focus ourattention on stage-oriented drama1.2 Features of Dramatic Language: Speakability & IndividualityAs a special form of literature, dramatic writing is largely different from other literarygenres. In Jiao Juyin’s words, the receptor of most literature genres, such as poetry andprose, is the text reader, while the receiver of drama includes not only the reader of theplaytext, but also the audience in the theatre. Thus the playwright needs to bear reader andaudience in mind at the same time. On this point, Robert Cohen also stated his opinion:“Because drama is often thought of as a form of literature and because many dramaticauthors begin as poets or novelists, it may be seen as if playwriting is primarily a literaryactivity. It is not. Etymology helps here: playwright is not playwrite. Writing for the theatreentails considerations not common to other literary forms.” Cohen, 2000: 82As a genre of literature, drama is mainly composed of stage directions and dramaticdialogueStage directions refer to the playwright’s imagination of the stage space Barranger,1986: 290. It is actually a description of intended paralinguistic instructions to directactors’ physical action. Stage directions can be divided into several categories, includingenvironmental description, setting description, description of characters’ facial expressions,mood and gestures. As a common role, stage directions are formal in style and concise inlanguageDramatic language, as the main content of a drama, is not merely an arrangement of2words on a page. It differs from other literary language in that it is “more than words on apage?it is the playwright’s blueprint of a special kind of experience, created to appeal asmuch to the eye as to the ear” Barranger, 1986: 89-90. It is a conceptualization of theinteractions of myriad elements in the theatrical medium: movement, speech, scenery,costume, staging, music, spectacle, and silence. As is said in An Introduction to Literature,drama is “not simply words but words spoken with accompanying gestures by performerswho are usually costumed in a particular setting” Barnet, Berm an and Burto, 1997: 536Dramatic dialogue is of essential importance in developing plots, creating characters,presenting crisis, describing circumstances and revealing the theme. The relationshipsbetween characters are, for the most time, constructed and developed through the languagethey use. Thus the creation of drama language becomes even harder. On the requirementsof dramatic language, many scholars have put forward their opinions, such as Nicoll’s“economical and artistic” Nicoll, 1985: 95, Backer’s “clear inmeaning, helpful to theadvancement of plots and in accordance with personalities” Backer, 2000: 426, LiJianwu’s “colloquial” Li, 1982:153, Lan Fan’s “actable, individual and poetic” Lan,1992: 474 and so on. Taking all these requirements into account, the most conspicuousfeatures of dramatic dialogue can be summarized into speakability and individualitySpeakability guarantees the effectiveness of being naturally spoken by actors and quicklyunderstood by the audience. And individuality defines the characterization of the wholedrama1.3 Duality of Drama Translation: Performance-oriented & Reader-orientedAs has been explored in previous sections, drama differs from other literature genres,for it is not only a linguistic art with reader-reception as its form of fulfillment, but also aperforming art with the theatre-goers as its ultimate receptor. The peculiarity of dramaresults in the duality of drama translation. Other than those general requirements forliterary translation, drama translation bears its own characteristicsAs a genre of literature, drama is loaded with the specificity of the culture it issituated in, like any other literary form. As we know, drama is to reflect real life and theproduction of drama is closely related to the life style and ideology of a certain society. To3put it in another way, drama, within hours’ performance, reflects the essence accumulatedin a culture and the seemingly concise dramatic text actually is loaded with plentifulcultural traits. Thus translator, as his mission determines, has to do his best to transmit thecultural information embedded in the original drama text, delivering the properties ofsource culture and conveying the aesthetic art of the source text as much as possibleWhile at the same time, drama is to be presented to the audience, the actualfulfillment of the essentiality of it depends as much on the extra-linguistic situation as onthe linguistic context. As a result, drama should not be translatedsimply as the text on thepage. The stage aspect of the play text should also be emphasized in drama translation, thatis, to ensure the performability of the source dramatic text on a foreign stage. According toBacker 2000: 51-52, performability means that theatrical needs are satisfied, and emotionis conveyed to audience within a certain time indirectly by actors rather than directly bythe playwright himself. But to naturally perform a foreign drama in a different context isnot an easy thing, for people from different cultures have different conventions andideologies. When translating other literary forms, we may resort to footnotes to solve thisproblem, but on the stage, it’s impossible for actors to read footnotes to the audienceTherefore adaptations to target language and culture are inevitable in drama translation,thus to avoid footnotes as well as difficulties in understanding Thus the drama translator is confronted with a central problem: to maintain theoriginal culture-bound message is a basic requirement for thetranslator. However, in orderto ensure the performability, adaptations have to be made and thus source culturalmessages will inevitably be affected. We may get a more thorough understanding of thedilemma in drama translation from A Text Book of Translation Newmark, 2004: 172:“The main purpose of translating a play is normally to have it performed successfullyTherefore a translator of drama inevitably has to bear the potential spectator in mindthough, here again, the better written and more significant the text, the fewer compromiseshe can make in favor of the reader. Further, he works under certain constraints: unlike thetranslator of fiction, he cannot gloss, explain puns or ambiguities or cultural references, nortranscribe words for the sake of local colour: his text is dramatic, with emphasis on verbs,rather than descriptive and explanatory.” 4In light of all these factors, due to the peculiarity of drama translation, traditional translation theory, which is mainly based on linguistic equivalence, could hardly help herein drama translation1.4 Relevant Study of Drama TranslationAlthough drama is the oldest genre of literature, academic study on drama translationonly got its start thirty years ago and still leaves much of its territory unexploredCompared with the study of the translation of other literary genres, study of dramatranslation lags way behind, and only a few scholars have systematically summarizedtheories of drama translation1.4.1 Drama Translation Theories in ChinaIn China, few works have been written on the central issues involved in translatingplays across languages. Yet we do have several scholars who have come up with someprinciples or theories concerning drama translation based on their own translation practicesAmong them the most prominent are Zhu Shenghao, Yu Guangzhong, and Ying Ruocheng1.4.1.1 Zhu ShenghaoMr. Zhu Shenghao, an excellent writer and translator in China, translated most ofShakespeare’s plays successfully into Chinese.In the preface to his translation ofShakespeare’s plays, he shared his experience in drama translation:While translating this book, I tried to maintain the verse of the original work to the utmost. Whenthat could not be achieved, I strained for resemblances, and lucidity and fluency are preferred inmy translated version to faithful reproduction of the original style. As for word-for-wordtranslation, I personally think poorly of this mechanical rendition. When the original text differsvastly from the Chinese version in grammatical structure, I’d rather adjust the sentence structure ofmy translation for the sake of intelligibility. After I translated a section, I would go through mytranslation as if I were a member of the audience and tried to see if there were any ambiguous andmisleading places. I would then act the translated play out as if I were an actor and see if the5translation read smooth and sounded melodious.A single hard word or sentence often may throwme into weeks of deliberationZhu, 1984: PrefaceHere Zhu Shenghao emphasizes some important aspects of drama translation: first,translation should try to preserve the original spirit; second,translation should be clear andeasy to understand; and third, translation should be smooth and easy to be pronounced bythe actors1.4.1.2 Yu GuangzhongYu Guangzhong has also summarized his tri-fold translation principle in the preface tohis translation of Oscar Wilde’s The Importance of Being Ernest: Fictional dialogue and dramatic dialogue are different in that readers can read the dialogue in afiction again and again for better comprehension, while theatre-goers can only listen to thedialogues in a play for one time. When certain information is missing, it’s gone for good. Itranslated this play not only for Chinese readers, but also for the Chinese spectators and actors,therefore I adopted a specific translation principle this time: I tried to make sure that my translationis pleasing to the eye of the readers, and pleasing to the ear of the audience, and easy to deliver byactors and actresses. I hope that my translated play turns out to be an animated drama-on-stagerather than a restrained closet-drama. Yu, 1983: PrefaceFor Yu Guangzhong, dialogues in novel and drama are written for different purposesso the translation of them should be done with different strategies. He emphasizes that thedialogue in a drama is to be heard by the audience and spoken by the actors, so a translatorshould bear in mind the principle of making his translation “pleasing to the eye of thereaders, pleasing to the ear of the audience, and easy to deliver by actors and actresses”1.4.1.3 Ying RuochengYing Ruocheng is a famous drama actor, director as well as translator. As an actor,Ying Ruocheng emphasizes the colloquialism in drama translation. In the preface to his6series of translated works, he points out some important features of drama translation andsummarizes his own principles for drama translatingA line spoken by an actor is transient; he cannot stop to annotate and explain, and this is the artisticessence of dramatic language…The dramatic language should be sonorous and forceful, whileobscurity and irrelevance should be avoided, so that an immediate effect can be produ ced…Theperformance on stage has its special requirements. What the audience wants to hear is clear andcrisp phrasing, neat and smart dialogue and verbal fights, which are available in a lot of greatworks by Oscar Wilde or Bernard Shaw. As a translator, we are responsible for presenting them infront of the audience. Therefore, colloquialism and brevity are the first and foremost principles indrama translation. Ying, 2001: PrefaceHere we can see, for Ying Ruocheng, colloquialism is important both for the sake ofthe actors and the audience, and brevity is to faithfully transfer the dramatic witticism inthe original text into the target languageThese statements on drama translation offer fresh insights into drama translation study, but the absence of a rigorous system of theory prevents them from being a solid foundationfor a systematic study of drama translation1.4.2 Drama Translation Theories in Western CountriesAt present there are mainly two principles prevailing in the fieldof drama translationOne is the “performability” standard, which derives from the semiotic ideas of drama. Theother is the “readability” one which is mainly held by Susan Bassnett, a well-knownscholar whose main focus is on the translation of deictic system in dramatic text1.4.2.1 George E. WellwarthIn his Special Considerations in Drama Translation, George E. Wellwarthsummarized the difficulties in drama translation into two principal points: “speakability”and styleGeorge defined “speakability” as “the degree of ease with which the words of the7translated text can be enunciated” qtd. in Rose, 1981: 140. The translation should soundwell on stage, and “li。

斯普林格数学研究生教材丛书

斯普林格数学研究生教材丛书《斯普林格数学研究生教材丛书》（Graduate Texts in Mathematics）GTM001《Introduction to Axiomatic Set Theory》Gaisi Takeuti, Wilson M.Zaring GTM002《Measure and Category》John C.Oxtoby（测度和范畴）（2ed.）GTM003《T opological Vector Spaces》H.H.Schaefer, M.P.Wolff（2ed.）GTM004《A Course in Homological Algebra》P.J.Hilton, U.Stammbach（2ed.）（同调代数教程）GTM005《Categories for the Working Mathematician》Saunders Mac Lane（2ed.）GTM006《Projective Planes》Daniel R.Hughes, Fred C.Piper（投射平面）GTM007《A Course in Arithmetic》Jean-Pierre Serre（数论教程）GTM008《Axiomatic set theory》Gaisi Takeuti, Wilson M.Zaring（2ed.）GTM009《Introduction to Lie Algebras and Representation Theory》James E.Humphreys（李代数和表示论导论）GTM010《A Course in Simple-Homotopy Theory》M.M CohenGTM011《Functions of One Complex VariableⅠ》John B.ConwayGTM012《Advanced Mathematical Analysis》Richard Beals GTM013《Rings and Categories of Modules》Frank W.Anderson, Kent R.Fuller（环和模的范畴）（2ed.）GTM014《Stable Mappings and Their Singularities》Martin Golubitsky, Victor Guillemin （稳定映射及其奇点）GTM015《Lectures in Functional Analysis and OperatorTheory》Sterling K.Berberian GTM016《The Structure of Fields》David J.Winter（域结构）GTM017《Random Processes》Murray RosenblattGTM018《Measure Theory》Paul R.Halmos（测度论）GTM019《A Hilbert Space Problem Book》Paul R.Halmos （希尔伯特问题集）GTM020《Fibre Bundles》Dale Husemoller（纤维丛）GTM021《Linear Algebraic Groups》James E.Humphreys （线性代数群）GTM022《An Algebraic Introduction to Mathematical Logic》Donald W.Barnes, John M.MackGTM023《Linear Algebra》Werner H.Greub（线性代数）GTM024《Geometric Functional Analysis and Its Applications》Paul R.HolmesGTM025《Real and Abstract Analysis》Edwin Hewitt, Karl StrombergGTM026《Algebraic Theories》Ernest G.ManesGTM027《General Topology》John L.Kelley（一般拓扑学）GTM028《Commutative Algebra》VolumeⅠOscar Zariski, Pierre Samuel（交换代数）GTM029《Commutative Algebra》VolumeⅡOscar Zariski, Pierre Samuel（交换代数）GTM030《Lectures in Abstract AlgebraⅠ.Basic Concepts》Nathan Jacobson（抽象代数讲义Ⅰ基本概念分册）GTM031《Lectures in Abs tract AlgebraⅡ.Linear Algabra》Nathan.Jacobson（抽象代数讲义Ⅱ线性代数分册）GTM032《Lectures in Abstract AlgebraⅢ.Theory of Fields and Galois Theory》Nathan.Jacobson（抽象代数讲义Ⅲ域和伽罗瓦理论）GTM033《Differential Topology》Morris W.Hirsch（微分拓扑）GTM034《Principles of Random Walk》Frank Spitzer（2ed.）（随机游动原理）GTM035《Several Complex Variables and Banach Algebras》Herbert Alexander, John Wermer（多复变和Banach代数）GTM036《Linear Topological Spaces》John L.Kelley, Isaac Namioka（线性拓扑空间）GTM037《Mathematical Logic》J.Donald Monk（数理逻辑）GTM038《Several Complex Variables》H.Grauert, K.Fritzshe GTM039《An Invitation to C*-Algebras》William Arveson （C*-代数引论）GTM040《Denumerable Markov Chains》John G.Kemeny, /doc/e96250642.htmlurie Snell, Anthony W.KnappGTM041《Modular Functions and Dirichlet Series in Number Theory》Tom M.Apostol （数论中的模函数和Dirichlet序列）GTM042《Linear Representations of Finite Groups》Jean-Pierre Serre（有限群的线性表示）GTM043《Rings of Continuous Functions》Leonard Gillman, Meyer JerisonGTM044《Elementary Algebraic Geometry》Keith KendigGTM045《Probabi lity TheoryⅠ》M.Loève（概率论Ⅰ）（4ed.）GTM046《Probability TheoryⅡ》M.Loève（概率论Ⅱ）（4ed.）GTM047《Geometric Topology in Dimensions 2 and 3》Edwin E.MoiseGTM048《General Relativity for Mathematicians》Rainer.K.Sachs, H.Wu伍鸿熙（为数学家写的广义相对论）GTM049《Linear Geometry》K.W.Gruenberg, A.J.Weir（2ed.）GTM050《Fermat's Last Theorem》Harold M.EdwardsGTM051《A Course in Differential Geometry》WilhelmKlingenberg（微分几何教程）GTM052《Algebraic Geometry》Robin Hartshorne（代数几何）GTM053《 A Course in Mathematical Logic for Mathematicians》Yu.I.Manin（2ed.）GTM054《Combinatorics with Emphasis on the Theory of Graphs》Jack E.Graver, Mark E.WatkinsGTM055《Introduction to Operator TheoryⅠ》Arlen Brown, Carl PearcyGTM056《Algebraic Topology：An Introduction》W.S.MasseyGTM057《Introduction to Knot Theory》Richard.H.Crowell, Ralph.H.FoxGTM058《p-adic Numbers, p-adic Analysis, and Zeta-Functions》Neal Koblitz（p-adic 数、p-adic分析和Z函数）GTM059《Cyclotomic Fields》Serge LangGTM060《Mathematical Methods of Classical Mechanics》V.I.Arnold（经典力学的数学方法）（2ed.）GTM061《Elements of Homotopy Theory》George W.Whitehead（同论论基础）GTM062《Fundamentals of the Theory of Groups》M.I.Kargapolov, Ju.I.Merzljakov GTM063《Modern Graph Theory》Béla BollobásGTM064《Fourier Series：A Modern Introduction》VolumeⅠ（2ed.）R.E.Edwards（傅里叶级数）GTM065《Differential Analysis on Complex Manifolds》Raymond O.Wells, Jr.（3ed.）GTM066《Introduction to Affine Group Schemes》William C.Waterhouse（仿射群概型引论）GTM067《Local Fields》Jean-Pierre Serre（局部域）GTM069《Cyclotomic FieldsⅠandⅡ》Serge LangGTM070《Singular Homology Theory》William S.MasseyGTM071《Riemann Surfaces》Herschel M.Farkas, Irwin Kra （黎曼曲面）GTM072《Classical Topology and Combinatorial Group Theory》John Stillwell（经典拓扑和组合群论）GTM073《Algebra》Thomas W.Hungerford（代数）GTM074《Multiplicative Number Theory》Harold Davenport （乘法数论）（3ed.）GTM075《Basic Theory of Algebraic Groups and Lie Algebras》G.P.HochschildGTM076《Algebraic Geometry：An Introduction to Birational Geometry of Algebraic Varieties》Shigeru Iitaka GTM077《Lectures on the Theory of Algebraic Numbers》Erich HeckeGTM078《A Course in Universal Algebra》Stanley Burris, H.P.Sankappanavar（泛代数教程）GTM079《An Introduction to Ergodic Theory》Peter Walters （遍历性理论引论）GTM080《A Course in_the Theory of Groups》Derek J.S.RobinsonGTM081《Lectures on Riemann Surfaces》Otto ForsterGTM082《Differential Forms in Algebraic Topology》Raoul Bott, Loring W.Tu（代数拓扑中的微分形式）GTM083《Introduction to Cyclotomic Fields》Lawrence C.Washington（割圆域引论）GTM084《A Classical Introduction to Modern Number Theory》Kenneth Ireland, Michael Rosen（现代数论经典引论）GTM085《Fourier Series A Modern Introduction》Volume 1（2ed.）R.E.Edwards GTM086《Introduction to Coding Theory》J.H.van Lint（3ed .）GTM087《Cohomology of Groups》Kenneth S.Brown（上同调群）GTM088《Associative Algebras》Richard S.PierceGTM089《Introduction to Algebraic and Abelian Functions》Serge Lang（代数和交换函数引论）GTM090《An Introduction to Convex Polytopes》Ame BrondstedGTM091《The Geometry of Discrete Groups》Alan F.BeardonGTM092《Sequences and Series in BanachSpaces》Joseph DiestelGTM093《Modern Geometry-Methods and Applications》（PartⅠ.The of geometry Surface s Transformation Groups and Fields）B.A.Dubrovin, A.T.Fomenko, S.P.Novikov （现代几何学方法和应用）GTM094《Foundations of Differentiable Manifolds and Lie Groups》Frank W.Warner（可微流形和李群基础）GTM095《Probability》A.N.Shiryaev（2ed.）GTM096《A Course in Functional Analysis》John B.Conway （泛函分析教程）GTM097《Introduction to Elliptic Curves and Modular Forms》Neal Koblitz（椭圆曲线和模形式引论）GTM098《Representations of Compact Lie Groups》Theodor Bre?cker, Tammo tom DieckGTM099《Finite Reflection Groups》L.C.Grove, C.T.Benson （2ed.）GTM100《Harmonic Analysis on Semigroups》Christensen Berg, Jens Peter Reus Christensen, Paul ResselGTM101《Galois Theory》Harold M.Edwards（伽罗瓦理论）GTM102《Lie Groups, Lie Algebras, and Their Representation》V.S.Varadarajan（李群、李代数及其表示）GTM103《Complex Analysis》Serge LangGTM104《Modern Geometry-Methods and Applications》（PartⅡ.Geometry and Topology of Manifolds）B.A.Dubrovin, A.T.Fomenko, S.P.Novikov（现代几何学方法和应用）GTM105《SL? (R)》Serge Lang（SL? (R)群）GTM106《The Arithmetic of Elliptic Curves》Joseph H.Silverman（椭圆曲线的算术理论）GTM107《Applications of Lie Groups to Differential Equations》Peter J.Olver（李群在微分方程中的应用）GTM108《Holomorphic Functions and Integral Representations in Several Complex Variables》R.Michael Range GTM109《Univalent Functions and Teichmueller Spaces》Lehto OlliGTM110《Algebraic Number Theory》Serge Lang（代数数论）GTM111《Elliptic Curves》Dale Husemoeller（椭圆曲线）GTM112《Elliptic Functions》Serge Lang（椭圆函数）GTM113《Brownian Motion and Stochastic Calculus》Ioannis Karatzas, Steven E.Shreve （布朗运动和随机计算）GTM114《A Course in Number Theory and Cryptography》Neal Koblitz（数论和密码学教程）GTM115《Differential Geometry：Manifolds, Curves, and Surfaces》M.Berger, B.Gostiaux GTM116《Measure and Integral》Volume1 John L.Kelley, T.P.SrinivasanGTM117《Algebraic Groups and Class Fields》Jean-Pierre Serre（代数群和类域）GTM118《Analysis Now》Gert K.Pedersen （现代分析）GTM119《An introduction to Algebraic Topology》Jossph J.Rotman（代数拓扑导论）GTM120《Weakly Differentiable Functions》William P.Ziemer（弱可微函数）GTM121《Cyclotomic Fields》Serge LangGTM122《Theory of Complex Functions》Reinhold RemmertGTM123《Numbers》H.-D.Ebbinghaus, H.Hermes, F.Hirzebruch, M.Koecher, K.Mainzer, J.Neukirch, A.Prestel, R.Remmert（2ed.）GTM124《Modern Geometry-Methods and Applications》（PartⅢ.Introduction to Homology Theory）B.A.Dubrovin, A.T.Fomenko, S.P.Novikov（现代几何学方法和应用）GTM125《Complex Variables：An introduction》Garlos A.Berenstein, Roger Gay GTM126《Linear Algebraic Groups》Armand Borel （线性代数群）GTM127《A Basic Course in Algebraic Topology》William S.Massey（代数拓扑基础教程）GTM128《Partial Differential Equations》Jeffrey RauchGTM129《Representation Theory：A First Course》William Fulton, Joe HarrisGTM130《T ensor Geometry》C.T.J.Dodson, T.Poston（张量几何）GTM131《A First Course in Noncommutative Rings》/doc/e96250642.htmlm（非交换环初级教程）GTM132《Iteration of Rational Functions：Complex Analytic Dynamical Systems》AlanF.Beardon（有理函数的迭代：复解析动力系统）GTM133《Algebraic Geometry：A First Course》Joe Harris （代数几何）GTM134《Coding and Information Theory》Steven Roman GTM135《Advanced Linear Algebra》Steven RomanGTM136《Algebra：An Approach via Module Theory》William A.Adkins, Steven H.WeintraubGTM137《Harmonic Function Theory》Sheldon Axler, Paul Bourdon, Wade Ramey（调和函数理论）GTM138《A Course in Computational Algebraic NumberTheory》Henri Cohen（计算代数数论教程）GTM139《T opology and Geometry》Glen E.BredonGTM140《Optima and Equilibria：An Introduction to Nonlinear Analysis》Jean-Pierre AubinGTM141《A Computational Approach to Commutative Algebra》Gr?bner Bases, Thomas Becker, Volker Weispfenning, Heinz KredelGTM142《Real and Functional Analysis》Serge Lang（3ed.）GTM143《Measure Theory》J.L.DoobGTM144《Noncommutative Algebra》Benson Farb, R.Keith DennisGTM145《Homology Theory：An Introduction to Algebraic Topology》James W.Vick（同调论：代数拓扑简介）GTM146《Computability：A Mathematical Sketchbook》Douglas S.BridgesGTM147《Algebraic K-Theory and Its Applications》Jonathan Rosenberg（代数K理论及其应用）GTM148《An Introduction to the Theory of Groups》Joseph J.Rotman（群论入门）GTM149《Foundations of Hyperbolic Manifolds》John G.Ratcliffe（双曲流形基础）GTM150《Commutative Algebra with a view toward Algebraic Geometry》David EisenbudGTM151《Advanced Topics in the Arithmetic of Elliptic Curves》Joseph H.Silverman（椭圆曲线的算术高级选题）GTM152《Lectures on Polytopes》Günter M.ZieglerGTM153《Algebraic Topology：A First Course》William Fulton（代数拓扑）GTM154《An introduction to Analysis》Arlen Brown, Carl PearcyGTM155《Quantum Groups》Christian Kassel（量子群）GTM156《Classical Descriptive Set Theory》Alexander S.KechrisGTM157《Integration and Probability》Paul MalliavinGTM158《Field theory》Steven Roman（2ed.）GTM159《Functions of One Complex Variable VolⅡ》John B.ConwayGTM160《Differential and Riemannian Manifolds》Serge Lang（微分流形和黎曼流形）GTM161《Polynomials and Polynomial Inequalities》Peter Borwein, Tamás Erdélyi（多项式和多项式不等式）GTM162《Groups and Representations》J.L.Alperin, Rowen B.Bell（群及其表示）GTM163《Permutation Groups》John D.Dixon, Brian Mortime rGTM164《Additive Number Theory：The Classical Bases》Melvyn B.NathansonGTM165《Additive Number Theory：Inverse Problems and the Geometry of Sumsets》Melvyn B.NathansonGTM166《Differential Geometry：Cartan's Generalization of Klein's Erlangen Program》R.W.SharpeGTM167《Field and Galois Theory》Patrick MorandiGTM168《Combinatorial Convexity and Algebraic Geometry》Günter Ewald（组合凸面体和代数几何）GTM169《Matrix Analysis》Rajendra BhatiaGTM170《Sheaf Theory》Glen E.Bredon（2ed.）GTM171《Riemannian Geometry》Peter Petersen（黎曼几何）GTM172《Classical Topics in Complex Function Theory》Reinhold RemmertGTM173《Graph Theory》Reinhard Diestel（图论）（3ed.）GTM174《Foundations of Real and Abstract Analysis》Douglas S.Bridges（实分析和抽象分析基础）GTM175《An Introduction to Knot Theory》W.B.Raymond LickorishGTM176《Riemannian Manifolds：An Introduction to Curvature》John M.LeeGTM177《Analytic Number Theory》Donald J.Newman（解析数论）GTM178《Nonsmooth Analysis and Control Theory》F.H.clarke, Yu.S.Ledyaev, R.J.Stern, P.R.Wolenski（非光滑分析和控制论）GTM179《Banach Algebra Techniques in Operator Theory》Ronald G.Douglas（2ed.）GTM180《A Course on Borel Sets》S.M.Srivastava（Borel 集教程）GTM181《Numerical Analysis》Rainer KressGTM182《Ordinary Differential Equations》Wolfgang Walter GTM183《An introduction to Banach Spaces》Robert E.MegginsonGTM184《Modern Graph Theory》Béla Bollobás（现代图论）GTM185《Using Algebraic Geomety》David A.Cox, John Little, Donal O’Shea（应用代数几何）GTM186《Fourier Analysis on Number Fields》Dinakar Ramakrishnan, Robert J.Valenza GTM187《Moduli of Curves》Joe Harris, Ian Morrison（曲线模）GTM188《Lectures on the Hyperreals：An Introduction to Nonstandard Analysis》Robert GoldblattGTM189《Lectures on Modules and Rings》/doc/e96250642.htmlm（模和环讲义）GTM190《Problems in Algebraic Number Theory》M.Ram Murty, Jody Esmonde（代数数论中的问题）GTM191《Fundamentals of Differential Geometry》Serge Lang（微分几何基础）GTM192《Elements of Functional Analysis》Francis Hirsch, Gilles LacombeGTM193《Advanced Topics in Computational Number Theory》Henri CohenGTM194《One-Parameter Semigroups for Linear Evolution Equations》Klaus-Jochen Engel, Rainer Nagel（线性发展方程的单参数半群）GTM195《Elementary Methods in Number Theory》Melvyn B.Nathanson（数论中的基本方法）GTM196《Basic Homological Algebra》M.Scott OsborneGTM197《The Geometry of Schemes》David Eisenbud, Joe HarrisGTM198《A Course in p-adic Analysis》Alain M.RobertGTM199《Theory of Bergman Spaces》Hakan Hedenmalm, Boris Korenblum, Kehe Zhu（Bergman空间理论）GTM200《An Introduction to Riemann-Finsler Geometry》D.Bao, S.-S.Chern, Z.Shen GTM201《Diophantine Geometry An Introduction》Marc Hindry, Joseph H.Silverman GTM202《Introduction to T opological Manifolds》John M.Lee GTM203《The Symmetric Group》Bruce E.SaganGTM204《Galois Theory》Jean-Pierre EscofierGTM205《Rational Homotopy Theory》Yves Félix, Stephen Halperin, Jean-Claude Thomas（有理同伦论）GTM206《Problems in Analytic Number Theory》M.Ram MurtyGTM207《Algebraic Graph Theory》Chris Godsil, Gordon Royle（代数图论）GTM208《Analysis for Applied Mathematics》Ward Cheney GTM209《A Short Course on Spectral Theory》William Arveson（谱理论简明教程）GTM210《Number Theory in Function Fields》Michael RosenGTM211《Algebra》Serge Lang（代数）GTM212《Lectures on Discrete Geometry》Jiri Matousek （离散几何讲义）GTM213《From Holomorphic Functions to Complex Manifolds》Klaus Fritzsche, Hans Grauert（从正则函数到复流形）GTM214《Partial Differential Equations》Jüergen Jost（偏微分方程）GTM215《Algebraic Functions and Projective Curves》David M.Goldschmidt（代数函数和投影曲线）GTM216《Matrices：Theory and Applications》Denis Serre （矩阵：理论及应用）GTM217《Model Theory An Introduction》David Marker（模型论引论）GTM218《Introduction to Smooth Manifolds》John M.Lee （光滑流形引论）GTM219《The Arithmetic of Hyperbolic 3-Manifolds》Colin Maclachlan, Alan W.Reid GTM220《Smooth Manifolds and Observables》Jet Nestruev（光滑流形和直观）GTM221《Convex Polytopes》Branko GrüenbaumGTM222《Lie Groups, Lie Algebras, and Representations》Brian C.Hall（李群、李代数和表示）GTM223《Fourier Analysis and its Applications》Anders Vretblad（傅立叶分析及其应用）GTM224《Metric Structures in Differential Geometry》Gerard Walschap（微分几何中的度量结构）GTM225《Lie Groups》Daniel Bump（李群）GTM226《Spaces of Holomorphic Functions in the Unit Ball》Kehe Zhu（单位球内的全纯函数空间）GTM227《Combinatorial Commutative Algebra》Ezra Miller, Bernd Sturmfels（组合交换代数）GTM228《A First Course in Modular Forms》Fred Diamond, Jerry Shurman（模形式初级教程）GTM229《The Geometry of Syzygies》David Eisenbud（合冲几何）GTM230《An Introduction to Markov Processes》Daniel W.Stroock（马尔可夫过程引论）GTM231《Combinatorics of Coxeter Groups》Anders Bjr?ner, Francesco Brenti（Coxeter 群的组合学）GTM232《An Introduction to Number Theory》Graham Everest, Thomas Ward（数论入门）GTM233《T opics in Banach Space Theory》Fenando Albiac, Nigel J.Kalton（Banach空间理论选题）GTM234《Analysis and Probability：Wavelets, Signals, Fractals》Palle E.T.Jorgensen（分析与概率）GTM235《Compact Lie Groups》Mark R.Sepanski（紧致李群）GTM236《Bounded Analytic Functions》John B.Garnett（有界解析函数）GTM237《An Introduction to Operators on the Hardy-Hilbert Space》Rubén A.Martínez-Avendano, Peter Rosenthal （哈代-希尔伯特空间算子引论）GTM238《A Course in Enumeration》Martin Aigner（枚举教程）GTM239《Number Theory：VolumeⅠT ools and Diophantine Equations》Henri Cohen GTM240《Number Theory：VolumeⅡAna lytic and Modern T ools》Henri Cohen GTM241《The Arithmetic of Dynamical Systems》Joseph H.SilvermanGTM242《Abstract Algebra》Pierre Antoine Grillet（抽象代数）GTM243《Topological Methods in Group Theory》Ross GeogheganGTM244《Graph Theory》J.A.Bondy, U.S.R.MurtyGTM245《Complex Analysis：In the Spirit of Lipman Bers》Jane P.Gilman, Irwin Kra, Rubi E.RodriguezGTM246《A Course in Commutative Banach Algebras》Eberhard KaniuthGTM247《Braid Groups》Christian Kassel, Vladimir TuraevGTM248《Buildings Theory and Applications》Peter Abramenko, Kenneth S.Brown GTM249《Classical Fourier Analysis》Loukas Grafakos（经典傅里叶分析）GTM250《Modern Fourier Analysis》Loukas Grafakos（现代傅里叶分析）GTM251《The Finite Simple Groups》Robert A.WilsonGTM252《Distributions and Operators》Gerd GrubbGTM253《Elementary Functional Analysis》Barbara D.MacCluerGTM254《Algebraic Function Fields and Codes》Henning StichtenothGTM255《Symmetry Representations and Invariants》Roe Goodman, Nolan R.Wallach GTM256《A Course in Commutative Algebra》Kemper GregorGTM257《Deformation Theory》Robin HartshorneGTM258《Foundation of Optimization》Osman GülerGTM259《Ergodic Theory：with a view towards Number Theory》Manfred Einsiedler, Thomas WardGTM260《Monomial Ideals》Jurgen Herzog, Takayuki Hibi GTM261《Probability and Stochastics》Erhan CinlarGTM262《Essentials of Integration Theory for Analysis》Daniel W.StroockGTM263《Analysis on Fock Spaces》Kehe ZhuGTM264《Functional Analysis, Calculus of Variations and Optimal Control》Francis ClarkeGTM265《Unbounded Self-adjoint Operatorson Hilbert Space》Konrad Schmüdgen GTM266《Calculus Without Derivatives》Jean-Paul PenotGTM267《Quantum Theory for Mathematicians》Brian C.HallGTM268《Geometric Analysis of the Bergman Kernel and Metric》Steven G.Krantz GTM269《Locally Convex Spaces》M.Scott Osborne。

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测度论测度论是研究一般集合上的测度和积分的理论。

它是勒贝格测度和勒贝格积分理论的进一步抽象和发展，又称为抽象测度论或抽象积分论，是现代分析数学中重要工具之一。

测度理论是实变函数论的基础。

定义测度理论是实变函数论的基础。

测度论所谓测度，通俗的讲就是测量几何区域的尺度。

我们知道直线上的闭区间的测度就是通常的线段长度；平面上一个闭圆盘的测度就是它的面积。

定理形成纵观勒贝格积分和勒贝格－斯蒂尔杰斯积分理论，不难发现它们都有三个基本要素。

第一，一个基本空间（即n维欧几里得空间Rη）以及这个空间的某些子集构成的集类即L（勒贝格）可测集或某L－S（勒贝格-斯蒂尔杰斯）可测集全体，这个集类对集的代数运算和极限运算封闭。

第二,一个与这个集类有关的函数类（即L可测函数或某L-S可测函数全体）。

第三,一个与上述集类有关的测度（即L测度或某L-S 测度）。

在三个要素的基础上，它们都是运用完全类似的定义和推理过程获得完全类似的一整套测度、可测函数、积分的定理（见勒贝格积分、贝尔函数）。

测度论正是基于这些基本共同点所形成一般理论一般定义对于更一般的集合，我们能不能定义测度呢？比如直线上所有有理数构成的集合，它的测度怎么衡量呢？一个简单的办法，就是先在每个有理点上找一个开区间覆盖它，就好比给它带个“帽子”。

因为有理数集是可列集（就是可以排像自然一样排好队，一个个数出来，也叫可数集，见集合论），所以我们可以让第n个有理数上盖的开区间长度是第一个有理数（比方是1）上盖的开区间长度的2^n分之一。

这样所有那些开区间的长度之和是个有限值（就是1上的开区间长度的2倍）。

现在我们让1上的开区间逐渐缩小趋向于一个点，那么所有区间的总长度也相应缩小，趋向于长度0。

这样我们就说有理数集的测度是0。

用上面这种方法定义的测度也叫外测度。

一个几何区域有了测度，我们就可以定义上面的函数的积分，这是推广的黎曼积分。

比如实数上的狄利克雷函数D(x)=1(如果x是有理数)，0（如果x是无理数）。

如果按照通常的理解，我们发现狄利克雷函数在整个数轴上的定积分不存在；但是按照上面讲的有理数的测度，我们就可以求出它的定积分是0。

实直线上的测度如下给出：设E是实数集，考虑可数个区间(aj,bj)满足对任何x∈E,都有某个j,使得x∈(aj,bj);考虑所有情形下和(b1-a1)+(b2-a2)+..的下确界称为E的外测度如果对任何集合F都有E∩F和F\E的外测度之和等于F的外测度，称E可测，定义其测度等于外测度直观含义上面的朋友已经解释过了数学定义测度的相关数学定义：集函数：设Ψ是上的非空集合类。

若对于每个一个A∈Ψ,都有一个实数或者±∞之一与之对应(为确定起见，下面假定只取+∞)，记为φ(A)，且至少有一个A∈Ψ,使得φ(A)取有限值，称φ(A)为定义在Ψ上的集函数。

(1)若对任意的正整数n以及任意的Ai∈Ψ，i=1，2……，n，Ai∩Aj=Ø(i≠j)，且(A1∪A2∪…Ai∪…An)∈Ψ，有φ(A1∪A2∪…Ai∪…An)=∑[φ(A1)∪φ(A2)∪…φ(Ai)∪…φ(An)]，则称φ在Ψ上具有有限可加性，也称φ是Ψ上的有限可加集函数。

(2)若对可列集的Ai∈Ψ，i=1，2……，n，Ai∩Aj=Ø(i≠j)，且(A1∪A2∪…Ai ∪…A∞)∈Ψ，有φ(A1∪A2∪…Ai∪…A∞)=∑[φ(A1)∪φ(A2)∪…φ(Ai)∪…φ(A∞)]，则称φ在Ψ上具有完全可加性或者б-可加性，也称φ是Ψ上的б-可加集函数或者广义测度。

(3)若对每一个A∈Ψ，φ(A)都取有限值，则称φ为上的有限集函数。

如果对每一个A ∈Ψ，存在一个集合序列⊂Ψ，使得A⊂(A1∪A2∪…Ai∪…A∞)，φ(An)<+∞，n=1，2，……则称φ是Ψ上的б-有限集函数。

(4)若集函数为有限可加且只取非负值则称为有限可加测度。

若集函数为б-可加，且只取非负值，则称为测度，用μ或ν表示。

具有性质Ω∈Ψ且ν(Ω)=1的测度，称为概率测度或者简称概率，一般用P表示。

相关定理此外，测度还可以取值于任何线性空间（通常带有一定拓扑，比如Banach空间），只要满足相应的可数可加性。

在Hilbert空间算子理论中还有所谓谱测度的概念，其中测度的取值为一固定Hilbert空间中投影算子的全体，且满足（在强意义下）的可数可加性。

如果测度空间X是拓扑空间而所考虑的б代数（或者б环，后者按照Halmos 《Measure Theory》）由全体紧集生成（这定义不是标准的；有的书上说是由全体开集生成），且测度在每个紧集上取有限值，则称为Borel测度。

如果Borel测度限制在所有能写成可数个开集的交的紧集生成的б环上，则称为Baire测度。

如果任何可测集E满足μ(E)=sup{μ(K): K含于E,K紧}=inf{μ(O):O包含E,O开}则称μ为正则测度。

Riesz-Markov表示定理：设X为局部紧T2空间，则对Cc(X)（即X上有紧支集的连续函数全体）上任何正线性泛函φ，存在正则Borel测度μ使得对任何f，φ(f)等于f关于μ的积分。

环和σ代数设X是非空的集。

E是以Χ的某些子集作为元素构成的集,称E为Χ上的一个集类。

设R是Χ上的一个集类。

如果它对集的并、差运算封闭，即对任何A、B∈R，必有A∪B∈R，A\B∈R，则称R为Χ上的环；如果R不仅是一个环，而且Χ∈R,则称R为Χ上的代数。

例如直线R1上的左开右闭的有限区间(α,b](α=b时,(α,b]表示空集）的全体记为P,P便是R1上的集类，但不是环。

P中任意有限个集的并的全体记为R0,R0便是R1上的环,但不是代数。

直线上任意有限个区间(包括无限区间)的并的全体R奿是R1上的代数。

环或代数虽对集的代数运算（即并、差、交运算）封闭，但对极限运算不一定封闭,这就不适应分析数学的要求。

因此,需要引入下面的概念：设φ)是Χ上的一个环,如果它对集的可列并运算封闭,则称φ)为Χ上的σ环;如果φ)是σ环,并且Χ∈φ),则称φ)为Χ上的σ代数。

σ环就对集的并、差、交以及极限运算都封闭,而σ代数还对集的求余集运算封闭。

例如，R0,R奿,都不是R1上的σ环，而L 可测集（或L-S可测集）的全体是R1上的σ代数。

又如Χ的一切子集的全体Χ是Χ上的σ代数。

由于任意个环的交仍是环,因此对一个集类E,一切包含E的环的交是包含E的最小环，记为R（E）。

同样,包含E的最小σ环记为φ)(E)。

可测空间和可测函数设φ)是Χ 上的σ环，称（Χ，φ)为可测空间，而称φ中的任何集A为(Χ,φ)中的可测集（也称为Χ中的φ可测集）。

如果Χ是Rn,而φ分别是Rn中L可测集全体（记为L）、由单调增加右连续函数g(x)生成的L-S可测集全体（记为Lg）、波莱尔集全体（记为B）,则相应地称(Χ,φ)是L可测空间、L-S可测空间、波莱尔可测空间。

设E是可测空间(Χ，φ))中的可测集，ƒ是定义在E上的有限实值函数。

如果对任何实数с，{Χ│ƒ(x)>с}∈φ，那么称ƒ为E上关于(Χ,φ)的可测函数，也称为E上的φ)可测函数。

这种可测函数是L可测函数、L-S可测函数等概念的直接推广。

它有许多等价定义方式,并且具有L可测涵数所具有的代数性质及极限性质。

定义在E上的复值函数ƒ，如果它的实部、虚部都是可测函数，那么就称ƒ为E上的可测函数。

可测空间、可测集、以及可测函数等概念原则上并不涉及测度。

测度和测度空间设Χ是非空集,E是Χ上的集类,定义在E上的函数称为集函数（因为自变元是属于E，它是Χ的子集式①）。

设R是Χ上的环，μ是定义在R上的取非负的广义实值(可以取值+∞)的集函数，如果满足：①μ(═)=0(═是空集)；②(可列可加性)对任何一列互不相交的An∈R(n=1,2…,),并且：式③式②①，有：式②=③，则称μ为环R上的测度。

设(Χ,φ)是一个可测空间,μ是定义在φ上的测度,则称(Χ,φ),μ)是测度空间。

特别,(R1,L,m)及(R1,Lg,mg)分别称为（直线上的）L 测度空间和L-S 测度空间。

测度空间(Χ,φ,μ)中的测度μ 除了平移、反射不变性以及余集(因为X可能不在S中）的性质外,具有勒贝格测度m的其他性质。

由于φ是σ环,对集的极限运算封闭，所以测度空间是建立具有良好的极限性质的积分的基础。

设A是可测空间(Χ，φ)中可测集。

如果有一列可测集{An},μ(An)<∞(n=1,2,…)，使得：式④，则称式④A为σ有限集。

如果φ)中一切集都是σ有限的,则称(Χ,φ),μ)是σ有限的测度空间。

特别，当φ是σ代数且Χ是σ有限集时,称(Χ,φ),μ)为全σ有限测度空间。

通常分析数学中所用的具体的(Χ,φ)，μ)大都是全σ有限测度空间。

设测度空间(Χ,φ),μ)中的φ)是σ代数,如果μ(Χ)<∞,则称(Χ,φ),μ)为全有限的测度空间。

特别,当μ(Χ)=1时，称(Χ,φ),μ)为概率测度空间（概率论中用的全是这种空间）。

设A是测度空间(Χ,φ),μ)上的可测集。

如果μ(A)=0，则称A为μ零集。

如果(Χ,φ),μ)中任何一个μ零集的任何子集都是可测集，则称（Χ，φ), μ）为完全测度空间。

例如(R1,L,m)，(R1,Lg,mg)都是完全的、全σ有限的测度空间。

测度空间上可测函数列的收敛同L测度一样,在测度空间(Χ,φ，μ)中也有命题P在E上“几乎处处”成立的概念，它是指E中使命题P不成立的点的全体（它可能不是可测集）包含在某个μ 零集中。

对于完全测度空间，命题P在E上几乎处处成立就是指使命题P不成立的点的全体是μ零集。

在不完全的测度空间上，关于μ几乎处处相等的两个可测函数ƒ和h，未必能从ƒ的可测性推出h也是可测的,只有在完全测度空间才能做到这一点。

对于测度空间上的可测函数序列，常用的重要收敛概念同样有两个:一是E上可测函数列{ƒn}几乎处处收敛于可测函数ƒ,即{x│ƒn(x)→ƒ(x)}包含在某个μ零集中;另一是E上可测函数列{ ƒn}度量收敛(或称依测度收敛)于可测函数ƒ，即对任何ε>0，式⑤，式⑤上述两种收敛的关系是和L测度的情形一样。

此外,在测度空间上也成立叶戈罗夫定理:设E上可测函数列{ƒn}几乎处处收敛于可测函数ƒ，并且μ(E)<∞ ，则对任何δ>0，必存在可测集Eδ嶅E,使得μ(E\Eδ)<δ,且{ƒn}在Eδ上一致收敛于ƒ。

类似于L测度的情形，在测度空间上也可引入度量基本序列（或依测度基本序列），并成立相应的完备性定理。

积分和积分平均收敛同L积分建立过程完全一样，可以建立测度空间上的积分概念,只要将那里的测度m换成现在的μ即可。

L积分所具有的大部分性质对一般的测度空间上的积分也是成立的。