Editorial Board
Gerald B. Folland
Robin Forman
Brad G. Osgood (Chair)
Michael Starbird
2000 Mathematics Subject Classification. Primary 28A20, 28A25, 42B05.
The images on the cover are representations of the ergodic transformations in
Chapter 7. The figure with the implied cardioid traces iterates of the squaring
map on the unit circle. The “spirograph” figures trace iterates of an irrational
rotation. The arc of + signs consists of iterates of an irrational rotation. I am
grateful to Edward Dunne for providing the figures.
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Library of Congress Cataloging-in-Publication Data
Franks, John M., 1943–
A (terse) introduction to Lebesgue integration / John Franks.
p. cm. (Student mathematical library ; v. 48)
Includes bibliographical references and index.
ISBN 978-0-8218-4862-3 (alk. paper)
1. Lebesgue integral. I. Title. II. Title: Introduction to Lebesgue integra-
QA312.F698 2009
515 .43–dc22 2009005870
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
publication is permitted only under license from the American Mathematical Society.
Requests for such permission should be addressed to the Acquisitions Department,
American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904-
2294, USA. Requests can also be made by e-mail to reprint-permission@ams.org.
2009 by John Franks. 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/
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