The general theory of integration:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
Oxford
Clarendon Press
1991
|
| Schriftenreihe: | Oxford mathematical monographs
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 262 S. |
| ISBN: | 019853566X |
Internformat
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Datensatz im Suchindex
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| adam_text | CONTENTS
0 Introduction and prerequisites 1
0.1 Introduction: the calculus, Lebesgue, and gauge
(Kurzweil Henstock) integrals 1
0.2 Basic definitions for simple set theory 7
0.3 Basic definitions for algebra 11
0.4 Basic definitions and theory for topology 13
0.5 Basic definitions and theory for order 26
0.6 Short history of integration 32
1 Division systems and division spaces 40
1.1 Definitions 40
1.2 The norm integral 47
1.3 The refinement integral 49
1.4 The gauge (Kurzweil Henstock) integral 50
1.5 The gauge integral, associated points at vertices, and infinite
intervals 52
1.6 McShane s modification, giving absolute integrals 54
1.7 Symmetric intervals 54
1.8 The divergence theorem 55
1.9 The general Denjoy integral 56
1.10 Burkill s approximate Perron integral 57
1.11 Division systems and spaces in a topology 58
2 Generalized Riemann and variational integration in
division systems and division spaces 59
2.1 Free division systems, the free p variation, free norm variation,
and corresponding variational integral, and the free
variation set 59
2.2 Freely decomposable division system 71
2.3 Division systems, the generalized Riemann and variational
integrals, the variation, and the variation set 74
2.4 Decomposable division systems 81
2.5 Division spaces 83
2.6 Decomposable division spaces and integration by substitution 91
2.7 Additive division spaces 92
2.8 Decomposable additive division spaces 101
X CONTENTS
2.9 Star sets and the intrinsic topology 103
2.10 Special results 112
3 Limits under the integral sign, functions depending
on a parameter 120
3.1 Introduction and necessary and sufficient conditions 120
3.2 Monotone sequences and functions 126
3.3 The bounded Riemann sums test and the majorized
(dominated) convergence test of Arzela and Lebesgue 134
4 Differentiation 142
4.1 The differentiation of strong variational integrals 142
4.2 Further results on differentiation 147
5 Cartesian products of a finite number of division
systems (spaces) 149
5.1 Fubini type results 149
5.2 Tonelli type results on the reversal of order of double
integrals 154
6 Integration in infinite dimensional spaces 157
6.1 Introduction 157
6.2 Division space integration 158
7 Perron type, Ward type, and convergence factor
integrals 167
7.1 Perron type integrals in fully decomposable division spaces 167
7.2 Ward integrals in decomposable division systems and spaces 171
7.3 Convergence factor integrals in fully decomposable division
spaces 173
8 Functional analysis and integration theory 184
8.1 Introduction 184
8.2 Young s inequality and Orlicz spaces 185
CONTENTS xi
8.3 The functional analysis of continuous generalized Riemann
integrals 199
8.4 Density integration 202
References 208
Name index 257
Subject index 260
|
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| bvnumber | BV004585771 |
| classification_rvk | SK 430 |
| ctrlnum | (OCoLC)260168736 (DE-599)BVBBV004585771 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004585771 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:14:38Z |
| institution | BVB |
| isbn | 019853566X |
| language | Undetermined |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002819395 |
| oclc_num | 260168736 |
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| physical | XI, 262 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Clarendon Press |
| record_format | marc |
| series2 | Oxford mathematical monographs |
| spelling | Henstock, Ralph 1923-2007 Verfasser (DE-588)118911406 aut The general theory of integration Ralph Henstock Oxford Clarendon Press 1991 XI, 262 S. txt rdacontent n rdamedia nc rdacarrier Oxford mathematical monographs Integralrechnung (DE-588)4027232-1 gnd rswk-swf Integral (DE-588)4131477-3 gnd rswk-swf Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Integral (DE-588)4131477-3 s DE-604 Integrationstheorie (DE-588)4138369-2 s Integralrechnung (DE-588)4027232-1 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002819395&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Henstock, Ralph 1923-2007 The general theory of integration Integralrechnung (DE-588)4027232-1 gnd Integral (DE-588)4131477-3 gnd Integrationstheorie (DE-588)4138369-2 gnd |
| subject_GND | (DE-588)4027232-1 (DE-588)4131477-3 (DE-588)4138369-2 |
| title | The general theory of integration |
| title_auth | The general theory of integration |
| title_exact_search | The general theory of integration |
| title_full | The general theory of integration Ralph Henstock |
| title_fullStr | The general theory of integration Ralph Henstock |
| title_full_unstemmed | The general theory of integration Ralph Henstock |
| title_short | The general theory of integration |
| title_sort | the general theory of integration |
| topic | Integralrechnung (DE-588)4027232-1 gnd Integral (DE-588)4131477-3 gnd Integrationstheorie (DE-588)4138369-2 gnd |
| topic_facet | Integralrechnung Integral Integrationstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002819395&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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