Gerald B. Folland
Brad G. Osgood (Chair)
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-
515 .43–dc22 2009005870
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copy a chapter for use in teaching or research. Permission is granted to quote brief
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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-
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2009 by John Franks. All rights reserved.
Printed in the United States of America.
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