Kai Lai Chung (鍾開萊) A Course in Probability Theory
In spite of the increasing flow of books on various topics in probability, there are almost no course textbooks like this one which, assuming a moderate background of measure theory but no knowledge of probability, cover the standard fundamental topics. The content of this book is orthodox, consisting of a thorough treatment of the usual topics connected with the idea of independence (sums of independent random variables, including a study of recurrence in random walks and associated notions, law of large numbers, central limit theorem with an estimate of the discrepancy, iterated logarithm law) and one chapter devoted to the Markov property (including the strong Markov property) and to the convergence theorems of martingale theory. No continuous parameter processes are considered. The treatment is along traditional lines but is meaty and sophisticated, and on occasion the author is not afraid to introduce elaborate computations. This book is definitely a course textbook, not a compendium of theorems. The subject has been pruned to the content of a two semester course. Although it starts from the beginning, the book is severely mathematical. Readers interested in applications or in permutation-coin-die-urn problems will have to look elsewhere. The book was intended to be and is a solid and clearly written mathematical textbook. The publisher is to be congratulated on the very readable composition.
Reviewer: Doob, J. L. [form MathSciNet]