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。

本书内容包括：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。

Preface to the third edition

Preface to the second edition

Preface to the first edition

1 Distribution function

 1.1 Monotone functions

 1.2 Distribution functions

 1.3 Absolutely continuous and singular distributions

2 Measure theory

 2.1 Classes of sets

 2.2 Probability measures and their distribution functions

3 Random variable. Expectation. Independence

 3.1 General definitions

 3.2 Properties of mathematical expectation

 3.3 Independence

4 Convergence concepts

 4.1 Various modes of convergence

 4.2 Almost sure convergence; Borel-Cantelli lemma

 4.3 Vague convergence

 4.4 Continuation

 4.5 Uniform integrability; convergence of moments

5 Law of large numbers. Random series

 5.1 Simple limit theorems

 5.2 Weak law of large numbers

 5.3 Convergence of series

 5.4 Strong law of large numbers

 5.5 Applications

 Bibliographical Note

6 Characteristic function

 6.1 General properties; convolutions

 6.2 Uniqueness and inversion

 6.3 Convergence theorems

 6.4 Simple applications

 6.5 Representation theorems

 6.6 Multidimensional case; Laplace transforms

 Bibliographical Note

7 Central limit theorem and its ramifications

 7.1 Liapounov's theorem

 7.2 Lindeberg-Feller theorem

 7.3 Ramifications of the central limit theorem

 7.4 Error estimation

 7.5 Law of the iterated logarithm

 7.6 Infinite divisibility

 Bibliographical Note

8 Random walk

 8.1 Zero-or-one laws

 8.2 Basic notions

 8.3 Recurrence

 8.4 Fine structure

 8.5 Continuation

 Bibliographical Note

9 Conditioning. Markov property. Martingale

 9.1 Basic properties of conditional expectation

 9.2 Conditional independence; Markov property

 9.3 Basic properties of smartingales4

 9.4 Inequalities and convergence 6

 9.5 Applications

 Bibliographical Note

Supplement: Measure and Integral

 1 Construction of measure

 2 Characterization of extensions

 3 Measures in R

 4 Integral

 5 Applications

General Bibliography

Index