文档介绍：The integrals of
'Lebesgue, Denjoy,
Perron, and Henstock
Russell A. Gordon
Graduate Studies.
in Mathematics
'Volume-4
American Mathematical Society
Graduate Studies in Mathematics VOL.
Graduate Studies
in Mathematics
Volume 4
The Integrals of Lebesgue,
Denjoy, Perron, and Henstock
Russell A. Gordon
air American Mathematical Society
Editorial Board
James E. Humphreys
Robion C. Kirby
Lance W. Small
1991 Mathematics Subject Classification. Primary 26Axx, 28Axx.
ABSTRACT. Suppose that f :[a, b] -+ R is differentiable at each point of [a, b]. Is f' integrable on
[a, b]? The answer to this question depends on the integral that is used. For example, the answer
is no for the Riemann and Lebesgue integrals. In this century, three integration processes have
been developed that provide an affirmative answer to this question. The principal investigators of
these integrals were Denjoy, Perron, and Henstock. Each of these integrals generalizes a different
property of the Lebesgue integral, but it turns out that all three integrals are equivalent.
In this book, the properties of the Lebesgue, Denjoy, Perron, and Henstock integrals are devel-
oped fully from their definitions. The equivalence of the last three integrals is then established.
Discussions of the integration by parts formula and convergence theorems are included. In the
last part of the book, we consider approximate derivatives and attempts to develop an integration
process for which every approximate derivative is integrable.
Library of Congress Cataloging-in-Publication Data
Gordon, Russell A., 1955-
The integrals of Lebesgue, Denjoy, Perron, and Henstock/Russell A. Gordon.
p. cm. -(Graduate studies in mathematics, ISSN 1065-7339; 4)
Includes bibliographical references and index.
ISBN 0-8218-3805-9
1. Measure . Functions of real . . Series.
515' .42--dc20 94-19080
CIP
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