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.