The integrals of Lebesgue, Denjoy, Perron, and Henstock /
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 sati...
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I. :
American Mathematical Society,
[1994]
|
| Series: | Graduate studies in mathematics ;
v. 4. |
| Subjects: | |
| Online Access: | Table of contents Inhaltstext |
| Summary: | 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. 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. Contains over 230 exercises (with solutions) that illustrate and expand the material in the text. |
|---|---|
| Physical Description: | xi, 395 pages : illustrations ; 27 cm. |
| Bibliography: | Includes bibliographical references (pages 389-390) and indexes. |
| ISBN: | 0821838059 9780821838051 |
| ISSN: | 1065-7339 ; |