Measure and Integral: Volume 1

✍ Scribed by John L. Kelley, T.P. Srinivasan

• Publisher: Springer
• Year: 2011
• Tongue: English
• Leaves: 162
• Series: Graduate Texts in Mathematics 116
• Edition: Softcover reprint of the original 1st ed. 1988
• Category: Library

✦ Synopsis

This book is a systematic exposition of the theory of measure and integration. It is intendend for students, and also as a reference work. The body of the text can be read by a student with a firm background in analysis, whereas the supplements treat more advanced topics, and require somewhat more maturity. Although the results given here are the standard ones, the authors have taken a new approach, systematically exploiting the concepts of -ring and -simplicity.

Content Level » Professional/practitioner

Related subjects » Analysis

✦ Table of Contents

Cover

Graduate Texts in Mathematics 116

Measure and Integralm Volume 1

Copyright
© 1988 by Springer-Verlag
ISBN 0-387-96633-1
QA312.K44 1988 515.4'2-dcl9
87-26571

PREFACE

CONTENTS

Chapter 0 PRELIMINARIES

 SETS

 FUNCTIONS

 COUNTABILITY

 ORDERINGS AND LATTICES

 CONVERGENCE IN R*

 UNORDERED SUMMABILI T Y

 HAUSDORFF MAXIMAL PRINCIPLE

Chapter 1 PRE-MEASURES

 SUPPLEMENT: G INVARIANT CONTENTS

 SUPPLEMENT: CARATHEODORY PRE-MEASURES

Chapter 2 PRE-MEASURE TO PRE-INTEGRAL

 SUPPLEMENT: PRE-INTEGRALS ON CJX) AND C0(X)

Chapter 3 PRE-INTEGRAL TO INTEGRAL

Chapter 4 INTEGRAL TO MEASURE

 SUPPLEMENT: L EBESG UE MEASURE A" FOR R"

 SUPPLEMENT: MEASURES ON B(X)

 SUPPLEMENT: G INVARIANT MEASURES

Chapter 5 MEASURABILITY AND a-SIMPLICITY

 SUPPLEMENT: STANDARD BOREL SPACES

Chapter 6 THE INTEGRAL Iµ ON L1(µ)

 SUPPLEMENT: BOREL MEASURES AND POSITIVE FUNCTIONALS

Chapter 7 INTEGRALS* AND PRODUCTS

 SUPPLEMENT: BOREL PRODUCT MEASURE

Chapter 8 MEASURES* AND MAPPINGS

 SUPPLEMENT: THE IMAGE OF Ap UNDERA SMOOTH MAP

 SUPPLEMENT: MAPS OF BOREL MEASURES*; CONVOLUTION

Chapter 9 SIGNED MEASURES AND INDEFINITE INTEGRALS

 SUPPLEMENT: DECOMPOSABLE MEASURES

 SUPPLEMENT: HAAR MEASURE

Chapter 10 BANACH SPACES

 SUPPLEMENT: THE SPACES Co (X)* AND L 1(p)*

 SUPPLEMENT: COMPLEX INTEGRAL AND COMPLEX MEASURE

 SUPPLEMENT: THE BOCHNER INTEGRAL

SELECTED REFERENCES

 ADDITIONAL TITLES

INDEX

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