Measure and integration:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Zürich
European Mathematical Society
[2016]
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| Series: | EMS textbooks in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 355 Seiten |
| ISBN: | 9783037191590 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface . ..... . ... . . . ... . . . ... . ... ... . . . . . v
Introduction . 1 ................ 1 ...... ..........., . . . 1
1 Abstract measure theory 3
1.1 a-algebras.......................................... 4
1.2 Measurable functions ............. ....... .... . . 11
1.3 Integration of nonnegative functions ................. 18
1.4 Integration of real valued functions ................. 32
1.5 Sets of measure zero ............................... 36
1.6 Completion of a measure space ...................... 43
1.7 Exercises . ...................................... 47
2 The Lebesgue measure ................... 57
2.1 Outer measures ................. . ; ............. . 58
2.2 The Lebesgue outer measure........................... 64
2.3 The transformation formula........................... 77
2.4 Lebesgue equals Riemann ...................... 86
2.5 Exercises........................................... 90
3 Borel measures.......................................... . 95
3.1 Regular Borel measures . . . . . . . ... . . . . .... . 95
3.2 Borel outer measures ................................ 107
3.3 The Riesz representation theorem .... .............. 113
3.4 Exercises ....... . . .......... . . ... ....... 126
4 Lp spaces ............................................................ 133
. 4.1 Holder and Minkowski . . ........................... . .......... 133
4.2 The Banach space LpQi) . ....................... 136
4.3 Separability..........................................—. . . . 141
4.4 Hilbert spaces............ ............... 147
4.5 The dual space of Lp(jjl) . ... : .1 ....... 152
4.6 Exercises . .................................................... 168
VIII
Contents
5 The Radon-Nikodym theorem............................................ 179
5.1 Absolutely continuous measures.................................. 179
5.2 The dual space of Lp(jjl) revisited............................. 187
5.3 Signed measures........................................... . . 197
5.4 Radon-Nikodym generalized ..................................... 205
5.5 Exercises....................................................... 214
6 Differentiation................................................... 221
6.1 Weakly integrable functions..................................... 221
6.2 Maximalfunctions ............................................. 227
6.3 Lebesgue points.............................................. . 233
6.4 Absolutely continuous functions............................... 239
6.5 Exercises ...................................................... 243
7 Product measures...............................................— 249
7.1 The product a-algebra.......................................... 249
7.2 The product measure............................................. 255
7.3 Fubini’s Theorem ............................................... 261
7.4 Fubini and Lebesgue............................................ 272
7.5 Convolution..................................................... 277
76 Marcinkiewicz interpolation..................................... 286
7.7 The Calderón-Zygmund inequality ................................ 292
7.8 Exercises..................................................... 304
8 The Haar measure . .................................................. 309
8.1 Topological groups ...................... . . . .............. 309
8.2 Haar measures ............................................... 312
Appendices
A Urysohn’s lemma ..................................................... 333
B The product topology.............................................. 339
C The Inverse function theorem .................................... . . . 343
Bibliography ........................................ 347
Index
351
|
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| discipline | Mathematik |
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| isbn | 9783037191590 |
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| physical | VIII, 355 Seiten |
| publishDate | 2016 |
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| spelling | Salamon, Dietmar 1953- Verfasser (DE-588)1015895271 aut Measure and integration Dietmar A. Salamon Zürich European Mathematical Society [2016] © 2016 VIII, 355 Seiten txt rdacontent n rdamedia nc rdacarrier EMS textbooks in mathematics Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Integrationstheorie (DE-588)4138369-2 s DE-604 Maßtheorie (DE-588)4074626-4 s Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029059313&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Salamon, Dietmar 1953- Measure and integration Integrationstheorie (DE-588)4138369-2 gnd Maßtheorie (DE-588)4074626-4 gnd |
| subject_GND | (DE-588)4138369-2 (DE-588)4074626-4 (DE-588)4151278-9 |
| title | Measure and integration |
| title_auth | Measure and integration |
| title_exact_search | Measure and integration |
| title_full | Measure and integration Dietmar A. Salamon |
| title_fullStr | Measure and integration Dietmar A. Salamon |
| title_full_unstemmed | Measure and integration Dietmar A. Salamon |
| title_short | Measure and integration |
| title_sort | measure and integration |
| topic | Integrationstheorie (DE-588)4138369-2 gnd Maßtheorie (DE-588)4074626-4 gnd |
| topic_facet | Integrationstheorie Maßtheorie Einführung |
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