Kai Lai Chung（钟开莱，1917－2009） 华裔数学家、概率学家。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”。
目錄：
Preface to the third edition iiiPreface to the second edition vPreface to the first edition vii1 Distribution function 1.1 Monotone functions 11.2 Distribution functions 71.3 Absolutely continuous and singular distributions 112 Measure theory2.1 Classes of sets 162.2 Probability measures and their distribution function 213 Random variable， Expectation.Independence3.1 General definition 343.2 Properties of mathematical expectation 413.3 Independence 534 Convergence concepts4.1 Various modes of convergence 684.2 Almost sure convergence; Borel-Cantelli lemma 754.3 Vague convergence 844.4 Continuation 914.5 Uniform untegrability; convergence of moments 995 Law of large numbers， Randrom series5.1 Simple limit theorems 1065.2 Weak low of large nymbers 1125.3 Convergence of serices 1215.4 Strong law of large numbers 1295.5 Applications 138Bibliographical Note 1486 Characteristic function6.1 General properties; convolutions 1506.2 Uniqueness and inversion 1606.3 Convergence theorems 1696.4 Simple applications 1756.5 Representation theorems 1876.6 Multidimentstional case; Laplace transforms 196Bibliographical Note 2047 Central limit theorem and its ramifications7.1 Liapounovs theorem 2057.2 Lindeberg-Feller theorem 2147.3 Ramifications of the central limit theorem 2247.4 Error estimation 2357.5 Law of the iterated logarithm 2427.6 Infinite divistibility 250Bibliographical Note 2618 Random walk8.1 Zero-or-one laws 2638.2 Basic notions 2708.3 Recurrence 2788.4 Fine structure 2888.5 Continuation 298Bibliographical Note 3089 Conditioning.Markov property. Martingale9.1 Basic properties of conditional expectation 3109.2 Conditional independence; Markov propery 3229.3 Basci properties of smartingales 3349.4 Inequalities and convergence 3469.5 Applications 360Bibliographical Note 373Supplement: Measure and Integral1 Construvtion of measure 3752 Characterization of extensions 3803 Measures in R 3874 Integral 3955 Applications 407General Bibliography 413Index 415
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