Steven G. Krantz
David Saltman (Chair)
2000 Mathematics Subject Classification. Primary 28-01;
Secondary 28A05, 28A10, 28A12, 28A15, 28A20, 28A25,
28A33, 28A35, 26A30, 26A42, 26A45, 26A46.
ABSTRACT. This text presents a motivated introduction to the theory of measure and integration.
Starting with an historical introduction to the notion of integral and a preview of the Riemann
integral, the reader is motivated for the need to study the Lebesgue measure and Lebesgue integral.
The abstract integration theory is developed via measure. Other basic topics discussed in the text
are Pubini's Theorem, Lp-spaces, Radon-Nikodym Theorem, change of variables formulas, signed
and complex measures.
Library of Congress Cataloging-in-Publication Data
Rana, Inder K.
An introduction to measure and integration / Inder K. Rana.—2nd ed.
p. cm. — (Graduate texts in mathematics, ISSN 1065-7339 ; v. 45)
Includes bibliographical references and index.
ISBN 0-8218-2974-2 (alk. paper)
1. Lebesgue integral. 2. Measure theory. I. Title. II. Graduate texts in mathematics ; 45.
QA312 .R28 2002
Copying and reprinting. Individual readers of this publication, and nonprofit libraries
acting for them, are permitted to make fair use of the material, such as to copy a chapter for use
in teaching or research. Permission is granted to quote brief passages from this publication in
reviews, provided the customary acknowledgment of the source is given.
Republication, systematic copying, or multiple reproduction of any material in this publica-
tion is permitted only under license from Narosa Publishing House. Requests for such permis-
sion should be addressed to Narosa Publishing House, 6 Community Centre, Panchscheel Park,
New Delhi 110 017, India.
First Edition © 1997 by Narosa Publishing House.
Second Edition © 2002 by Narosa Publishing House. All rights reserved.
Printed in the United States of America.
@ The paper used in this book is acid-free and falls within the guidelines
established to ensure permanence and durability.
Visit the AMS home page at http://www.ams.org/
10 9 8 7 6 5 4 3 2 1 07 06 05 04 03 02