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.
  • chapter Chapter 1|20 pages

    Introduction and Preliminaries

    chapter Chapter 2|89 pages

    Measurability and Measures

    chapter Chapter 3|37 pages

    Measurable Functions

    chapter Chapter 4|108 pages

    Classical Integration

    chapter Chapter 5|109 pages

    Differentiation and Duality

    chapter Chapter 6|88 pages

    Product Measures and Integrals

    chapter Chapter 7|111 pages

    Nonabsolute Integration

    chapter Chapter 8|36 pages

    Capacity Theory and Integration

    chapter Chapter 9|32 pages

    The Lifting Theorem

    chapter Chapter 10|72 pages

    Topological Measures

    chapter Chapter 11|30 pages

    Some Complements and Applications