概率论教程（英文版·第3版）

　　随机变量和分布函数，测度论，数学期望，方差，各种收敛性，大数律， 中心极限定理，特征函数，随机游动， 马氏性和鞅理论.本书内容丰富，逻辑紧密，叙述严谨，不仅可以扩展读者的视野，而且还将为其后续的学习和研究打下坚实基础。此外，本书的习题较多， 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。
　　 本书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。本书内容丰富，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，本书的习题较多, 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

　　In this new edition, I have added a Supplement on Measure and Integral.The subject matter is first treated in a general setting pertinent to an abstract measure space, and then specified in the classic Borel-Lebesgue case for the real line. The latter material, an essential part of real analysis, is presupposed in the original edition published in 1968 and revised in the second edition of 1974. When I taught the course under the title "Advanced Probability"at Stanford University beginning in 1962, students from the departments of statistics, operations research (formerly industrial engineering), electrical engineering, etc. often had to take a prerequisite course given by other instructors before they enlisted in my course. In later years I prepared a set of notes,lithographed and distributed in the class, to meet the need. This forms the basis of the present Supplement. It is hoped that the result may as well serve in an introductory mode, perhaps also independently for a short course in the stated topics.
　　 The presentation is largely self-contained with only a few particular references to the main text. For instance, after (the old) 2.1 where the basic notions of set theory are explained, the reader can proceed to the first two sections of the Supplement for a full treatment of the construction and completion of a general measure; the next two sections contain a full treatment of the mathematical expectation as an integral, of which the properties are recapitulated in 3.2. In the final section, application of the new integral to the older Riemann integral in calculus is described and illustrated with some famous examples. Throughout the exposition, a few side remarks, pedagogic, historical, even judgmental, of the kind I used to drop in the classroom, are approximately reproduced.
　　In drafting the Supplement, I consulted Patrick Fitzsimmons on several occasions for support. Giorgio Letta and Bernard Bru gave me encouragement for the uncommon approach to Borel's lemma in ~3, for which the usual proof always left me disconsolate as being too devious for the novice's appreciation.
　　A small number of additional remarks and exercises have been added to the main text.
　　Warm thanks are due: to Vanessa Gerhard of Academic Press who deciphered my handwritten manuscript with great ease and care; to Isolde Field of the Mathematics Department for unfailing assistence; to Jim Luce for a mission accomplished. Last and evidently not least, my wife and my daughter Corinna performed numerous tasks indispensable to the undertaking of this publication.