| Description |
1 online resource (vii, 140 pages) |
| Series |
Series in real analysis ; v. 8 |
|
Series in real analysis ; v. 8.
|
| Contents |
Preface; CONTENTS; 0. Introduction; 1. Basic concepts and properties of y-integration; 1.1 Notation.; 1.2 Lemma (Cousin).; 1.3 Definition.; 1.4 Theorem.; 1.5 Definition.; 1.6 Theorem.; 1.7 Lemma (Saks Henstock).; 1.8 Definition.; 1.9 Theorem.; 1.10 Note.; 1.11 Definition.; 1.12 Theorem.; 1.13 Lemma.; 1.14 Theorem.; 1.15 Lemma.; 1.16 Theorem.; 2. Convergence; 2.1. Theorem.; 2.2 Definition.; 2.3 Lemma.; 2.4 Lemma.; 2.5 Lemma.; 2.6 Definition.; 2.7 Lemma.; 2.8 Lemma.; 2.9 Theorem.; 2.10 Theorem.; 2.11 Definition.; 2.12 Theorem.; 2.13 Lemma.; 2.14 Definition.; 2.15 Lemma.; 2.16 Theorem |
|
3. Convergence and locally convex spaces3.1 Preliminaries.; 3.2 Lemma.; 3.3 Definition.; 3.4 Notation.; 3.5 Lemma.; 3.6 Note.; 3.7 Theorem.; 3.8 Lemma.; 3.9 Theorem.; 3.10 Lemma.; 3.11 Lemma.; 3.12 Lemma.; 3.13 Lemma.; 3.14 Theorem; 3.15 Lemma.; 4. An auxiliary locally convex space; 4.1 Preliminaries.; 4.2 Theorem.; 4.3 Lemma.; 4.4 Lemma.; 4.5 Lemma.; 4.6 Notation.; 4.7 Lemma.; 4.8 Theorem.; 5. L-integration; 5.1 Preliminaries.; 5.2 Theorem.; 5.3 Theorem.; 5.4 Lemma.; 5.5 Lemma.; 5.6 Lemma.; 5.7 Lemma.; 5.8 Example.; 5.9 Theorem.; 5.10 Remark.; 5.11 Remark.; 5.12 Theorem.; 6. .M-integration |
|
6.1 Notation. 6.2 Definition.; 6.3 Theorem.; 6.4 Definition.; 6.5 Lemma.; 6.6.; 6.7 Lemma.; 6.8 Lemma.; 6.9 Lemma.; 6.10 Lemma.; 6.11 Lemma.; 6.12 Lemma.; 7. Noncompleteness; 7.1 A restriction on y.; 7.2 Lemma.; 7.3 Theorem.; 7.4 Lemma.; 7.5 Notation and some observations.; 7.6 Lemma.; 7.7 Lemma.; 7.8 Lemma.; 7.9 Lemma.; 7.10 Theorem.; 8. S-integration; 8.1 Preliminaries.; 8.2 Theorem.; 8.3 Theorem.; 8.4 Lemma.; 8.5 Lemma.; 8.6 Lemma.; 8.7 Lemma.; 8.8 Remark .; 8.9 Theorem.; 8.10 Theorem.; 8.11 Theorem.; 8.12 Lemma.; 9. R-integration; 9.1 Preliminaries.; 9.2 Theorem.; 9.3 Notation.; 9.4 Lemma |
|
9.5 Note. 10. An extension of the concept of y-integration; 10.1 Introduction.; 10.2 Definition.; 10.3 Definition.; 10.4 X(S*)-integration.; 10.5 Remark.; 10.6 X(R*)-integration.; 11. Differentiation and integration; 11.1 Definition.; 11.2 Definition.; 11.3 Theorem.; 11.4 Theorem.; 11.5 Remarks.; 11.6 Notation.; 11.7 Theorem.; 11.8 Theorem.; 11.9 Theorem.; 11.10 Theorem.; 11.11 Lemma.; 11.12 Theorem.; 11.13 Theorem.; 11.14 Remark.; 11.15 Remark.; 11.16 Theorem.; References; List of symbols; Index |
| Summary |
The main topics of this book are convergence and topologization. Integration on a compact interval on the real line is treated with Riemannian sums for various integration bases. General results are specified to a spectrum of integrations, including Lebesgue integration, the Denjoy integration in the restricted sense, the integrations introduced by Pfeffer and by Bongiorno, and many others. Morever, some relations between integration and differentiation are made clear. The book is self-contained. It is of interest to specialists in the field of real functions, and it can also be read by student |
| Bibliography |
Includes bibliographical references (page 135) and indexes |
| Notes |
English |
|
Print version record |
| Subject |
Lebesgue integral.
|
|
Henstock-Kurzweil integral.
|
|
Vector spaces.
|
|
MATHEMATICS -- Calculus.
|
|
MATHEMATICS -- Mathematical Analysis.
|
|
Henstock-Kurzweil integral
|
|
Lebesgue integral
|
|
Vector spaces
|
|
Lebesgue-Integral
|
|
Lebesgue, Intégrale de.
|
|
Henstock-Kurzweil, Intégrales de.
|
| Form |
Electronic book
|
| LC no. |
2002512064 |
| ISBN |
9789812777195 |
|
9812777199 |
|
1281929549 |
|
9781281929549 |
|
9786611929541 |
|
6611929541 |
|
