| 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”。 |
| 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 bibliographical note supplement: measure and integral general bibliography index |
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