Derivation and integration:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2001
|
| Edition: | 1. publ. |
| Series: | Cambridge tracts in mathematics
140 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 266 S. |
| ISBN: | 0521792681 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface xi
Acknowledgements xv
1. Preliminaries 1
1.1. The setting 1
1.2. Topology 4
1.3. Measures 11
1.4. Covering theorems 16
1.5. Densities 21
1.6. Lipschitz maps 27
1.7. BV functions 29
1.8. BV sets 34
1.9. Slices of BV sets 39
1.10. Approximating BV sets 42
2. Charges 47
2.1. The definition and examples 47
2.2. Spaces of charges 57
2.3. Derivates 60
2.4. Derivability 67
2.5. Reduced charges 76
2.6. Partitions 82
3. Variations of charges 90
3.1. Some classical concepts 90
3.2. The essential variation 97
3.3. The integration problem 106
3.4. An excursion to Hausdorff measures 109
3.5. The critical variation 118
ix
x Contents
3.6. AC, charges 124
3.7. Essentially clopen sets 130
4. Charges and BV functions 135
4.1. The charge F x L1 135
4.2. The space (CH*(E),S) 142
4.3. Duality 148
4.4. More on BV functions 154
4.5. The charge FLg 162
4.6. Lipeomorphisms 173
5. Integration 186
5.1. The R integral 186
5.2. Multipliers 192
5.3. Change of variables 197
5.4. Averaging 205
5.5. The Riemann approach 209
5.6. Charges as distributional derivatives 217
5.7. The Lebesgue integral 223
6. Extending the integral 229
6.1. Buczolich s example 229
6.2. X convergence 236
6.3. The GR integral 240
6.4. Additional properties 246
Bibliography 255
List of symbols 259
Index 263
|
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| discipline | Mathematik |
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| id | DE-604.BV013876538 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:53:37Z |
| institution | BVB |
| isbn | 0521792681 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009493144 |
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| physical | XVI, 266 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Pfeffer, Washek F. Verfasser aut Derivation and integration Washek F. Pfeffer 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2001 XVI, 266 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 140 Integral (DE-588)4131477-3 gnd rswk-swf Verallgemeinerung (DE-588)4316262-9 gnd rswk-swf Integral (DE-588)4131477-3 s Verallgemeinerung (DE-588)4316262-9 s DE-604 Cambridge tracts in mathematics 140 (DE-604)BV000000001 140 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009493144&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pfeffer, Washek F. Derivation and integration Cambridge tracts in mathematics Integral (DE-588)4131477-3 gnd Verallgemeinerung (DE-588)4316262-9 gnd |
| subject_GND | (DE-588)4131477-3 (DE-588)4316262-9 |
| title | Derivation and integration |
| title_auth | Derivation and integration |
| title_exact_search | Derivation and integration |
| title_full | Derivation and integration Washek F. Pfeffer |
| title_fullStr | Derivation and integration Washek F. Pfeffer |
| title_full_unstemmed | Derivation and integration Washek F. Pfeffer |
| title_short | Derivation and integration |
| title_sort | derivation and integration |
| topic | Integral (DE-588)4131477-3 gnd Verallgemeinerung (DE-588)4316262-9 gnd |
| topic_facet | Integral Verallgemeinerung |
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