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Measure Theory and Integration, Second Edition : Chapman & Hall/CRC Pure and Applied Mathematics - M. M. Rao

Measure Theory and Integration, Second Edition

Chapman & Hall/CRC Pure and Applied Mathematics

By: M. M. Rao

Hardcover

Published: 1st January 2004
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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-CarathA(c)odory 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.

"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

Preface to the Second Editionp. v
Preface to the First Editionp. xi
Introduction and Preliminariesp. 1
Motivation and Outlookp. 1
The Space R[superscript n] as a Modelp. 4
Abstraction of the Salient Featuresp. 14
Measurability and Measuresp. 21
Measurability and Class Propertiesp. 21
The Lebesgue Outer Measure and the Caratheodory Processp. 30
Extensions of Measures to Larger Classesp. 67
Distinction between Finite and Infinite Measuresp. 86
Metric Outer Measuresp. 92
Lebesgue-Stieltjes Measuresp. 99
Measurable Functionsp. 110
Definition and Basic Propertiesp. 110
Measurability with Measures and Convergencep. 120
Image Measures and Vague Convergencep. 136
Classical Integrationp. 147
The Abstract Lebesgue Integralp. 147
Integration of Nonmeasurable Functionsp. 163
The Lebesgue Limit Theoremsp. 171
The Vitali-Hahn-Saks Theorem and Signed Measuresp. 191
The L[superscript p]-spacesp. 203
The Four Basic Theorems of Banach Spacesp. 238
Differentiation and Dualityp. 255
Variations of Set Functions and the Hahn Decompositionp. 255
Absolute Continuity and Complete Monotonicity of Functionsp. 268
The Radon-Nikodym Theorem: Sigma-Finite Casep. 296
The Radon-Nikodym Theorem: General Casep. 320
Duality of L[superscript p]-spaces and Conditional Expectationsp. 330
Product Measures and Integralsp. 364
Basic Definitions and Propertiesp. 364
The Fubini-Stone and Tonelli Theoremsp. 381
Remarks on Non-Cartesian Productsp. 398
Infinite Product Measuresp. 405
Two Applications of Infinite Productsp. 437
Nonabsolute Integrationp. 452
Nonabsolute Integration on the Linep. 453
Product Spaces and P-Integrationp. 488
Vector Integrationp. 502
Boundedness Principles for Nonabsolute Integrationp. 517
Some Complementsp. 549
Capacity Theory and Integrationp. 563
Preliminaries on Analytic Setsp. 563
Capacity: A Construction and Choquet's Theoremp. 570
Application to the Daniell Integralp. 585
The Lifting Theoremp. 599
The problem, Motivation, and Preliminariesp. 599
Existence Proof for the Lifting Mapp. 611
Topologies Induced by Lifting and Related Conceptsp. 622
Topological Measuresp. 631
Introduction and Preliminariesp. 631
Regularity of Measuresp. 639
Local Functionals and the Riesz-Markov Theoremp. 667
Haar Measuresp. 687
Some Complements and Applicationsp. 703
Lattice and Homomorphism Propertiesp. 703
Some Applications of the Stone Isomorphism Theoremp. 713
Remarks on Topology of a Group Through Measurep. 729
Appendixp. 733
Referencesp. 737
Index of Symbols and Notationp. 747
Author Indexp. 751
Subject Indexp. 755
Table of Contents provided by Rittenhouse. All Rights Reserved.

ISBN: 9780824754013
ISBN-10: 0824754018
Series: Chapman & Hall/CRC Pure and Applied Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 792
Published: 1st January 2004
Publisher: Taylor & Francis Inc
Country of Publication: US
Dimensions (cm): 22.9 x 15.2  x 4.1
Weight (kg): 1.27
Edition Number: 2
Edition Type: New edition