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Rating: 
Summary: the best buy
Review: "A course in probability theory", written by Kai Lai Chung, has been referred by not only mathematicians but also mathematical economists.This book is written very rigorously, but almost all of the theorems have easy-to-understand proofs. So it is not difficult to follow. Moreover, there are lots of exercises in this book. So I do recommend this book.
Rating:
Summary: A well organized textbook
Review: There are several nice books in Grad-level Probability Theory. Billingsley's "Probability and Measure" is the richest one, but somehow poor organized and unpleasant printing. Resnick's "Probability Path" serve best for those who has no time to prepare first in measure theory and Lebesque integration but sacrifice some detail in latter part of the book. If you don't have previous Real Analysis training, I would suggest read Resnick first, and then find Billingsley for reference. But if you already good at measure and integration, Kai Lai Chung's "A Course in Probability Theory" still the best textbook teach step by step without losing detail. Chung's style is friendly to self studying like Resnick, but cover more detail in latter part of the book than Resnick. Chung's book is the best companion fot typical one semester course regradless what textbook your teacher choose. In the other words , Resnick helps students significantly in first half of the semester, Chung helps in the whole semester, and Billingsley may offer best effort after you took the Probability Theory course.
Rating: 
Summary: excellent text on probability
Review: This text by Chung was one of the texts that I used when I was taking a graduate course in probability at Stanford in 1975. It is carefully written but challenging. It provides good coverage of the central limit theorem, the law of large numbers and the law of the iterated logarithm. It also covers stable laws very well. The style is one of rigorous mathematics with theorems, and lemmas given with their mathematical proofs.The book was recently revised. The revised text does not change much but new material on measure and integration that is now commonly included in the first graduate course in probability has been added. In the 1970s at Stanford a course in measure theory was a prerequisite for the course in advanced probability although some student took it concurrently. If you plan to get this text, the revised edition is probably worth it. If you already have this edition and know your measure theory, it may not be worth it to get the new edition.
Rating:
Summary: excellent text on probability
Review: This text by Chung was one of the texts that I used when I was taking a graduate course in probability at Stanford in 1975. It is carefully written but challenging. It provides good coverage of the central limit theorem, the law of large numbers and the law of the iterated logarithm. It also covers stable laws very well. The style is one of rigorous mathematics with theorems, and lemmas given with their mathematical proofs. The book was recently revised. The revised text does not change much but new material on measure and integration that is now commonly included in the first graduate course in probability has been added. In the 1970s at Stanford a course in measure theory was a prerequisite for the course in advanced probability although some student took it concurrently. If you plan to get this text, the revised edition is probably worth it. If you already have this edition and know your measure theory, it may not be worth it to get the new edition.
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