本书的主要内容如下：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。

钟开莱（1917-2009），浙江杭州人，生于上海，华裔数学家。1936年进入清华大学物理系，1940年毕业于西南联合大学数学系，之后留校任讲师。他先师从华罗庚，后转投许宝绿（数理统计和概率论领域第一位具有国际声望的中国数学家）学习概率论。1944年获得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。二十世纪五十年代任教于美国纽约州雪城（Syracuse）大学，六十年代以后任斯坦福大学数学系教授、系主任、名誉教授。据不完全统计，他直接指导的博士生有15位左右，间接的学术晚辈则超过400位。钟开莱有十余部著作，其清晰的逻辑和严谨的叙述，使得许多教材已经成为享誉世界的经典，影响了几代学生。

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 function
3 Random variable, Expectation.Independence
3.1 General definition
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 untegrability; convergence of moments
5 Law of large numbers, Randrom series
5.1 Simple limit theorems
5.2 Weak low of large nymbers
5.3 Convergence of serices
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 Multidimentstional 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 divistibility
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 propery
9.3 Basci properties of smartingales
9.4 Inequalities and convergence
9.5 Applications
Bibliographical Note
Supplement: Measure and Integral
1 Construvtion of measure
2 Characterization of extensions
3 Measures in R
4 Integral
5 Applications
General Bibliography
Index