Gerald B. Folland - Real Analysis: Modern Techniques and Their Applications

Real Analysis

PURE AND APPLIED MATHEMATICS

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BURKLebesgue Measure and Integration: An Introduction

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Library of Congress Cataloging-in-Publication Data:

Folland, Gerald B.
Real analysis : modern techniques and their applications / Gerald B. Folland. 2nd ed.
p. cm. (Pure and applied mathematics)
A Wiley-Interscience publication.
Includes bibliographical references and index.
ISBN 0-471-31716-0 (cloth : alk. paper)
1. Mathematical analysis. 2. Functions of real variables.
I. Title. II. Series: Pure and applied mathematics (John Wiley & Sons: Unnumbered)
QA300.F67 1999
515dc21
9837260

To the memory of my mother and father
Helen B. Folland
and
Harold F. Folland

Preface

The name real analysis is something of an anachronism. Originally applied to the theory of functions of a real variable, it has come to encompass several subjects of a more general and abstract nature that underlie much of modern analysis. These general theories and their applications are the subject of this book, which is intended primarily as a text for a graduate-level analysis course. Chapters 1 through 7 are devoted to the core material from measure and integration theory, point set topology, and functional analysis that is a part of most graduate curricula in mathematics, together with a few related but less standard items with which I think all analysts should be acquainted. The last four chapters contain a variety of topics that are meant to introduce some of the other branches of analysis and to illustrate the uses of the preceding material. I believe these topics are all interesting and important, but their selection in preference to others is largely a matter of personal predilection.

The things one needs to know in order to read this book are as follows: