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Convergence of Probability Measures (Wiley Series in Probability and Statistics)

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When I was a graduate student at Stanford in the late 1970s I took a course in stochastic processes from Sid Resnick. Patrick Billingsley is an excellent probabilist who has written some very clear texts on probability theory and measure theory. In studying asymptotic distribution theory for independent or dependent data convergence in probability is a very important problem and Billingsley was the master at explaining it as well as the other major probability convergence criteria. So we relied heavily on Billingsley's two books on the convergence of probability measures. This text was in its first edition and was referred to as Big Bill because it was the more detailed of the two books. The other which came in paperback was simpler and more concise. That one we called Little Bill. Although we tended to find what we needed in Little Bill, Big Bill was useful also.

A classic, will survive through the ages as long as Real Analysis and Probability are studied by students the world over. You need it to get a fundamental grounding in Probability Theory