The Riemann approach to integration: local geometric theory
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1993
|
| Edition: | 1. publ. |
| Series: | Cambridge tracts in mathematics
109 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 302 S. |
| ISBN: | 0521440351 |
Staff View
MARC
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| 245 | 1 | 0 | |a The Riemann approach to integration |b local geometric theory |c Washek F. Pfeffer |
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Record in the Search Index
| _version_ | 1804123965764927488 |
|---|---|
| adam_text | Contents
Preface page xi
Acknowledgments xv
I One dimensional integration
1 Preliminaries 3
1.1 Lengths 4
1.2 Partitions 5
1.3 Stieltjes sums 7
2 The McShane integral 8
2.1 The integral 8
2.2 Absolute integrability 12
2.3 Convergence theorems 17
2.4 Connections with derivatives 24
2.5 Gap functions 30
2.6 Integration by parts 32
3 Measure and measurability 37
3.1 Extended real numbers 37
3.2 Measures 38
3.3 Measurable sets 44
3.4 Calculating measures 52
3.5 Negligible sets 55
3.6 Measurable functions 56
3.7 The a^ measure 60
4 Integrable functions 64
4.1 Integral and measure 64
4.2 Semicontinuous functions 69
4.3 The Perron test 71
4.4 Approximations 77
5 Descriptive definition 81
5.1 AC functions 81
5.2 Covering theorems 86
viii Contents
5.3 Differentiation 91
5.4 Singular functions 98
6 The Henstock Kurzweil integral 102
6.1 The P integral 102
6.2 Integration by parts 108
6.3 Connections with measures 111
6.4 AC* functions 115
6.5 Densities 118
6.6 Almost differentiable functions 120
6.7 Gages and calibers 124
II Multidimensional integration
7 Preliminaries 133
7.1 Intervals 134
7.2 Volumes 136
7.3 Partitions 139
7.4 Stieltjes sums 141
8 The McShane integral 143
8.1 The integral 143
8.2 Dirac volumes 146
8.3 The divergence theorem 148
8.4 Measures and measurability 153
8.5 The Perron test 158
8.6 The Fubini theorem 161
9 Descriptive definition 168
9.1 AC functions 168
9.2 Covering theorems 170
9.3 Derivability 174
10 Change of variables 180
10.1 Integrating over a set 180
10.2 Luzin maps 185
10.3 Lipschitz maps 188
10.4 The Rademacher theorem 193
10.5 The main formula 198
10.6 Almost differentiable maps 203
Contents be
11 The gage integral 207
11.1 A motivating example 207
11.2 Continuous additive functions 211
11.3 Gages and calibers 214
11.4 The g integral 218
11.5 Improper integrals 225
11.6 Connections with the McShane integral 228
11.7 Almost derivable functions 230
12 The ^ integral 239
12.1 Shape and regularity 239
12.2 The ^ integral 242
12.3 Derivability relative to T 246
12.4 Integration by parts 251
12.5 The quasi Hausdorff measure 253
12.6 Solids 258
12.7 Change of variables 261
12.8 Multipliers 265
13 Recent developments 273
13.1 The 5 integral 273
13.2 The perimeter 278
13.3 The flux 285
13.4 The £V integral 287
Bibliography 293
List of symbols 296
Index 299
|
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| id | DE-604.BV009626187 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:38:09Z |
| institution | BVB |
| isbn | 0521440351 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006361628 |
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| physical | XIV, 302 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Pfeffer, Washek F. Verfasser aut The Riemann approach to integration local geometric theory Washek F. Pfeffer 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1993 XIV, 302 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 109 Riemannsches Integral (DE-588)4049996-0 gnd rswk-swf Riemannsches Integral (DE-588)4049996-0 s DE-604 Cambridge tracts in mathematics 109 (DE-604)BV000000001 109 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006361628&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pfeffer, Washek F. The Riemann approach to integration local geometric theory Cambridge tracts in mathematics Riemannsches Integral (DE-588)4049996-0 gnd |
| subject_GND | (DE-588)4049996-0 |
| title | The Riemann approach to integration local geometric theory |
| title_auth | The Riemann approach to integration local geometric theory |
| title_exact_search | The Riemann approach to integration local geometric theory |
| title_full | The Riemann approach to integration local geometric theory Washek F. Pfeffer |
| title_fullStr | The Riemann approach to integration local geometric theory Washek F. Pfeffer |
| title_full_unstemmed | The Riemann approach to integration local geometric theory Washek F. Pfeffer |
| title_short | The Riemann approach to integration |
| title_sort | the riemann approach to integration local geometric theory |
| title_sub | local geometric theory |
| topic | Riemannsches Integral (DE-588)4049996-0 gnd |
| topic_facet | Riemannsches Integral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006361628&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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