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Henstock-Kurzweil integration : its relation to topological vector spaces

Author: Jaroslav Kurzweil
Publisher: Singapore ; River Edge, NJ : World Scientific, ©2000.
Series: Series in real analysis, v. 7.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Henstock-Kurzweil (HK) integration, which is based on integral sums, can be obtained by an inconspicuous change in the definition of Riemann integration. It is an extension of Lebesgue integration and there exists an HK-integrable function f such that its absolute value.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Kurzweil, Jaroslav.
Henstock-Kurzweil integration.
Singapore ; River Edge, NJ : World Scientific, ©2000
(OCoLC)44588898
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jaroslav Kurzweil
ISBN: 9789812793843 9812793844
OCLC Number: 826660242
Description: 1 online resource (vi, 136 pages).
Contents: PREFACE; CONTENTS; INTRODUCTION; 1. INTEGRABLE FUNCTIONS AND THEIR PRIMITIVES; 1.1 Notation; 1.2 Lemma; 1.3 Definition; 1.4 Definition; 1.5 Note; 1.6 Definition; 1.7 Note; 1.8 Lemma; 1.9 Lemma; 1.10 Lemma; 1.11 Lemma; 1.12 Theorem; 1.13 Definition; 1.14 Note; 1.15 Lemma; 1.16 Lemma; 1.17 Theorem; 1.18 Theorem; 1.19 Theorem; 1.20 Theorem; 2. GAUGES AND BOREL MEASURABILITY; 2.1.; 2.2.; 2.3 Lemma.; 2.4.; 2.5 Lemma.; 2.6 Lemma.; 2.7 Lemma.; 2.8.; 2.9 Lemma.; 2.10 Lemma.; 2.11 Lemma.; 2.12.; 2.13 Theorem.; 2.14 Definition.; 2.15 Theorem.; 2.16.; 2.17 Theorem.; 3. CONVERGENCE; 3.1 Theorem.; 3.2. 3.3.3.5 Definition.; 3.6 Lemma.; 3.7 Theorem.; 3.8 Definition.; 3.9 Theorem.; 3.10 Theorem.; 3.11 Definition.; 3.12 Theorem.; 3.13 Definition.; 3.14 Theorem.; 4. AN ABSTRACT SETTING; 4.1.; 4.2 Lemma.; 4.3 Definition.; 4.4 Theorem.; 4.5 Theorem.; 4.6 Theorem.; 4.7.; 4.8.; 4.9 Lemma.; 4.10.; 4.11 Theorem.; 5. AN ABSTRACT SETTING WITH D COUNTABLE; 5.1.; 5.2 Theorem.; 5.3 Lemma.; 5.4 Lemma.; 5.5 Lemma.; 5.6.; 5.7 Theorem.; 5.8 Examples.; 5.9 Note.; 5.10 Note.; 5.11.; 6. LOCALLY CONVEX TOPOLOGIES TOLERANT TO Q-CONVERGENCE; 6.1.; 6.2.; 6.3 Lemma.; 6.4 Lemma.; 6.5 Lemma.; 6.6.; 6.7 Theorem. 7. TOPOLOGICAL VECTOR SPACES TOLERANT TO Q-CONVERGENCE7.1.; 7.2.; 7.3 Theorem.; 7.4 Theorem.; 7.5 Definition.; 7.6.; 7.7 Lemma.; 7.8 Lemma.; 7.9 Lemma.; 7.10 Lemma.; 7.11 Theorem.; 8. P AS A COMPLETE TOPOLOGICAL VECTOR SPACE; 8.1 Notation.; 8.2 Theorem.; 8.3.; 8.4 Lemma.; 8.5 Lemma.; 8.6 Lemma.; 8.7 Lemma.; 8.8 Lemma.; 8.9 Lemma.; 8.10 Lemma.; 8.11 Lemma.; 8.12 Lemma.; 8.13 Lemma.; 8.14 Lemma.; 8.15 Lemma.; 8.16 Theorem; 8.17 Theorem; 8.18 Theorem; 8.19 Theorem; 8.20; 8.21 Lemma.; 8.22.; 8.23 Lemma.; 8.24; 8.25 Lemma.; 8.26; 8.27 Lemma.; 9. OPEN PROBLEMS; 9.1.; 9.2.; APPENDIX; A.1 Filters. A.2 Topology. A.3.; A.4 Definition.; A.5 Theorem.; A.6 Definition.; A.7 Definition.; A.8 Theorem.; A.9 Theorem.; A.10 Definition.; A.11 Definition.; A. 12 Theorem.; List of symbols; INDEX; REFERENCES.
Series Title: Series in real analysis, v. 7.
Responsibility: Jaroslav Kurzweil.

Abstract:

An analysis of Henstock-Kurzweil (HK) integration and its relation to topological vector spaces. HK integration is treated only on compact one-dimensional intervals and the set of convergent  Read more...

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