This book provides a thorough exposition of the main concepts and results related to various types of convergence of measures arising in measure theory, probability theory, functional analysis, partial differential equations, mathematical physics, and other theoretical and applied fields. Particular attention is given to weak convergence of measures. The principal material is oriented toward a broad circle of readers dealing with convergence in distribution of random variables and weak convergence of measures. The book contains the necessary background from measure theory and functional analysis. Large complementary sections aimed at researchers present the most important recent achievements. More than 100 exercises (ranging from easy introductory exercises to rather difficult problems for experienced readers) are given with hints, solutions, or references. Historic and bibliographic comments are included.

Bibliographic references

Includes bibliographical references (pages 253-282) and index.

Contents

Weak convergence of measures on Rd

Convergence of measures on metric spaces

Metrics on spaces of measures

Convergence of measures on topological spaces

Spaces of measures with the weak topology.

ISBN

9781470447380 ((hardcover ; : alkaline paper))

147044738X ((hardcover ; : alkaline paper))

LCCN

2018024621

OCLC

1043957348

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