A comprehensive, self-contained, yet easily accessible presentation of basic concepts, examining measure-theoretic foundations as well as analytical tools. Covers classical as well as modern methods, with emphasis on the strong interrelationship between probability theory and mathematical analysis, and with special stress on the applications to statistics and analysis. Includes recent developments, numerous examples and remarks, and various end-of-chapter problems. Notes and comments at the end of each chapter provide valuable references to sources and to additional reading material.
Table of Contents
Basic Concepts of Probability Theory.
The Laws of Large Numbers.
Distribution and Characteristic Functions.
Some Further Results on Characteristic Functions.
The Central Limit Problem.
Random Variables Taking Values in a Normed Linear Space.
Some Frequently Used Symbols and Abbreviations.
Author and Subject Indexes.