ABSTRACT

Written by one of the best-known probabilists in the world this text offers a clear and modern presentation of modern probability theory and an exposition of the interplay between the properties of metric spaces and those of probability measures. This text is the first at this level to include discussions of the subadditive ergodic theorems, metrics for convergence in laws and the Borel isomorphism theory. The proofs for the theorems are consistently brief and clear and each chapter concludes with a set of historical notes and references. This book should be of interest to students taking degree courses in real analysis and/or probability theory.

chapter 1|18 pages

Foundations; Set Theory

chapter 2|44 pages

General Topology

chapter 3|23 pages

Measures

chapter 4|30 pages

Integration

chapter 6|28 pages

Convex Sets and Duality of Normed Spaces

chapter 7|22 pages

Measure, Topology, and Differentiation

chapter 8|26 pages

Introduction to Probability Theory

chapter 10|38 pages

Conditional Expectations and Martingales

chapter 12|37 pages

Stochastic Processes