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。

作者简介

Kai Lai Chung（钟开莱，1917-2009）华裔数学家、概率学家。浙江杭州人。1917年生于上海。1936年考入清华大学物理系。1940年毕业于西南联合大学数学系，之后任西南联合大学数学系助教。1944年考取第六届庚子赔款公费留美奖学金。1945年底赴美国留学。1947年获普林斯顿大学博士学位。20世纪50年代任教于美国纽约州Syracuse大学，60年代以后任斯坦福大学数学系教授、系主任、名誉教授。钟开莱著有十余部专著。为世界公认的20世纪后半叶“概率学界学术教父”。

内页插图

Index
Preface to the third editioniii
Preface to the second editionv
Preface to the first editionvii
1 Distribution function
1.1 Monotone functionsl
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 Liapounovs theorem
7.2 Lindeberg-FeUer 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 expectation3 l
9.2 Conditional independence; Markov property
9.3 Basic properties of smartingales
9.4 Inequalities and convergence
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

前言/序言

　　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 engi- neering, 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 refer- ences 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 mathe- matical 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.

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