測度論と積分 Measure Theory and Integration（2）

著者名：Rao, M.M.

CRC Press（2018/10/03発売）

• 言語：ENG
• ISBN：9780824754013
• eISBN：9781351991483
• NDC分類：413

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.

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