概率论教程

《概率论教程:英文版(第3版)》是一本享誉世界的经典概率论教材，令众多读者受益无穷。自出版以来。已被世界75％以上的大学的数万名学生使用。《概率论教程:英文版(第3版)》内容丰富，逻辑清晰，叙述严谨。不仅可以拓展读者的视野。而且还将为其后续的学习和研究打下坚实基础。此外，《概率论教程:英文版(第3版)》的习题较多，都经过细心的遴选，从易到难，便于读者巩固练习。本版补充了有关测度和积分方面的内容，并增加了一些习题。

preface to the third edition iii preface to the second edition v preface to the first edition vii 1 distribution function 1.1 monotone functions 1 1.2 distribution functions 7 1.3 absolutely continuous and singular distributions 11 2 measure theory 2.1 classes of sets 16 2.2 probability measures and their distribution functions 21 3 random variable. expectation. independence 3.1 general definitions 34 3.2 properties of mathematical expectation 41 3.3 independence 53 4 convergence concepts 4.1 various modes of convergence 68 4.2 almost sure convergence; borel-cantelli lemma 75 4.3 vague convergence 84 4.4 continuation 91 4.5 uniform integrability; convergence of moments 99 5 law of large numbers. random series 5.1 simple limit theorems 106 5.2 weak law of large numbers 112 5.3 convergence of series 121 5.4 strong law of large numbers 129 5.5 applications 138 bibliographical note 148 8 characteristic function 6.1 general properties; convolutions 150 6.2 uniqueness and inversion 160 6.3 convergence theorems 169 6.4 simple applications 175 6.5 representation theorems 187 6.6 multidimensional case; laplace transforms 196 bibliographical note 204 7 central limit theorem and its ramifications 7.1 liapounov's theorem 205 7.2 lindeberg-feller theorem 214 7.3 ramifications of the central limit theorem 224 7.4 error estimation 235 7.5 law of the iterated logarithm 242 7.6 infinite divisibility 250 bibliographical note 261 8 random walk 8.1 zero-or-one laws 263 8.2 basic notions 270 8.3 recurrence 278 8.4 fine structure 288' 8.5 continuation 298 bibliographical note 308 9 conditioning. markov property. martingale 9.1 basic properties of conditional expectation 310 9.2 conditional independence; markov property 322 9.3 basic properties of smartingales 334 9.4 inequalities and convergence 346 9.5 applications 360 bibliographical note 373 supplement: measure and integral 1 construction of measure 375 2 characterization of extensions 380 3 measures in r 387 4 integral 395 5 applications 407 general bibliography 413 index 415