James Humphreys (Chair)
2000 Mathematics Subject Classification. Primary 26-01;
Secondary 26A39, 26A42, 28-01.
ABSTRACT. This book gives an introduction to integration theory via the "generalized Riemann
integral" due to Henstock and Kurzweil. The class of integrable functions coincides with those
of Denjoy and Perron and includes all conditionally convergent improper integrals as well as the
Lebesgue integrable functions. Using this general integral the author gives a full treatment of the
Lebesgue integral on the line.
The book is designed for students of mathematics and of the natural sciences and economics. An
understanding of elementary real analysis is assumed, but no familiarity with topology or measure
theory is needed. The author provides many examples and a large collection of exercises—many
Library of Congress Cataloging-in-Publication Data
Bartle, Robert Gardner, 1927-
A modern theory of integration / Robert G. Bartle.
p. cm. — (Graduate studies in mathematics ; v. 32)
Includes bibliographical references and indexes.
ISBN 0-8218-0845-1 (alk. paper)
1. Integrals. I. Title. II. Series.
QA312 .B32 2001
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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 Assistant to the Publisher, American Mathematical Society,
P. O. Box 6248, Providence, Rhode Island 02940-6248. Requests can also be made by e-mail to
© 2001 by the American Mathematical Society. All rights reserved.
The American Mathematical Society retains all rights
except those granted to the United States Government.
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.
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