Measure Theory and Integration: 2nd Edition (Hardback) book cover

Measure Theory and Integration

2nd Edition

By M.M. Rao

CRC Press

792 pages

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Hardback: 9780824754013
pub: 2004-01-30
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Description

Significantly revised and expanded, this authoritative reference/text comprehensively describes concepts in measure theory, classical integration, and generalized Riemann integration of both scalar and vector types-providing a complete and detailed review of every aspect of measure and integration theory using valuable examples, exercises, and applications.

With more than 170 references for further investigation of the subject, this Second Edition

  • provides more than 60 pages of new information, as well as a new chapter on nonabsolute integrals

  • contains extended discussions on the four basic results of Banach spaces

  • presents an in-depth analysis of the classical integrations with many applications, including integration of nonmeasurable functions, Lebesgue spaces, and their properties

  • details the basic properties and extensions of the Lebesgue-Carathéodory measure theory, as well as the structure and convergence of real measurable functions

  • covers the Stone isomorphism theorem, the lifting theorem, the Daniell method of integration, and capacity theory

    Measure Theory and Integration, Second Edition is a valuable reference for all pure and applied mathematicians, statisticians, and mathematical analysts, and an outstanding text for all graduate students in these disciplines.

  • Reviews

    "Significantly revised and expanded, this authoritative reference/text comprehensively describes concepts in measure theory, classical integration, and generalized Riemann integration of both scalar and vector types - providing a complete and detailed review of every aspect of measure and integration theory[,] offering valuable examples, exercises, and applications. This book examines the Henstock-Kurzweil integral with approaches not found in any other text."

    - L'Enseignement Mathematique, Vol. 50, 1-2, Jan-Jun 2004

    "This monograph provides a significantly revised and expanded version of the original edition published in 1987 on the classical topics in measure theory and integration. …The book is well understandable and requires only a basic knowledge of advanced calculus….It can be warmly recommended to a broad spectrum of reader - to graduate students as well as young researchers who wish to become acquainted with the basic elements and deeper properties of abstract analysis and its applications."

    -EMS Newsletter, March 2006

    Table of Contents

    Introduction and Preliminaries

    Measurability and Measures

    Measurable Functions

    Classical Integration

    Differentiation and Duality

    Product Measures and Integrals

    Nonabsolute Integration

    Capacity Theory and Integration

    The Lifting Theorem

    Topological Measures

    Some Complements and Applications

    Appendix

    References

    Index of Symbols and Notation

    Author Index

    Subject Index

    About the Series

    Chapman & Hall/CRC Pure and Applied Mathematics

    Learn more…

    Subject Categories

    BISAC Subject Codes/Headings:
    MAT037000
    MATHEMATICS / Functional Analysis