Asymptotic distribution theorems in probability and statistics have always depended on the classical theory of weak convergence of distribution functions in Euclidean space - convergence, at continuity points of the limit function. The 20th century has seen the creation and extensive application of a more inclusive theory of weak convergence of probability measures on metric spaces. There are many asymptotic results that can be formulated within this classical theory but require, for their proofs, this more general theory, which thus does not merely study itself.

Praise for the Third Edition

-It is, as far as I'm concerned, among the best books in math ever written....if you are a mathematician and want to have the top reference in probability, this is it.- (Amazon.com, January 2006)

A complete and comprehensive classic in probability and measure theory

Probability and Measure, Anniversary Edition by Patrick Billingsley celebrates the achievements and advancements that have made this book a classic in its field for the past 35 years. Now re-issued in a new style and format, but with the reliable...