Integration between the Lebesgue integral and the Henstock-Kurzweil integral : its relation to local convex vector spaces /

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 th...

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Bibliographic Details
Main Author: Kurzweil, Jaroslav.
Format: eBook
Language:English
Published: Singapore ; River Edge, N.J. : World Scientific, ©2002.
Series:Series in real analysis ; v. 8.
Subjects:
Online Access:CONNECT
CONNECT
Table of 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.