Graduate Studies in Mathematics
Volume: 4; 1994; 395 pp; Hardcover
MSC: Primary 26; 28;
Print ISBN: 978-0-8218-3805-1
Product Code: GSM/4
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Electronic ISBN: 978-1-4704-2066-6
Product Code: GSM/4.E
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The Integrals of Lebesgue, Denjoy, Perron, and Henstock

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Russell A. Gordon

This book provides an elementary, self-contained presentation of the integration processes developed by Lebesgue, Denjoy, Perron, and Henstock. The Lebesgue integral and its essential properties are first developed in detail. The other three integrals are all generalizations of the Lebesgue integral that satisfy the ideal version of the Fundamental Theorem of Calculus: if $F$ is differentiable on the interval $[a,b]$, then $F'$ is integrable on $[a,b]$ and $\int _a^b F'= F(b) - F(a)$. One of the book's unique features is that the Denjoy, Perron, and Henstock integrals are each developed fully and carefully from their corresponding definitions. The last part of the book is devoted to integration processes which satisfy a theorem analogous to the Fundamental Theorem, in which $F$ is approximately differentiable. This part of this book is preceded by a detailed study of the approximate derivative and ends with some open questions. This book contains over 230 exercises (with solutions) that illustrate and expand the material in the text. It would be an excellent textbook for first-year graduate students who have background in real analysis.

Readership

First year graduate students in mathematics.

The Integrals of Lebesgue, Denjoy, Perron, and Henstock

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Title (HTML): The Integrals of Lebesgue, Denjoy, Perron, and Henstock

Author(s) (Product display): Russell A. Gordon

Affiliation(s) (HTML): Whitman College, Walla Walla, WA

Abstract:

Book Series Name: Graduate Studies in Mathematics

Volume: 4

Publication Month and Year: 1994-08-01

Page Count: 395

Cover Type: Hardcover

Print ISBN-13: 978-0-8218-3805-1

Online ISBN 13: 978-1-4704-2066-6

Print ISSN: 1065-7339

Online ISSN: 1065-7339

Primary MSC: 26; 28

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Readership:

First year graduate students in mathematics.

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- Copyright
Contents
- Contents
Preface
- Preface
Chapter 1. Lebesgue Measure
- Chapter 1. Lebesgue Measure

The Integrals of Lebesgue, Denjoy, Perron, and Henstock

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The Integrals of Lebesgue, Denjoy, Perron, and Henstock

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Cover

Title

Copyright

Contents

Preface

Chapter 1. Lebesgue Measure