Integration theory:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Chapman & Hall
1997
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Chapman & Hall mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 294 S. |
| ISBN: | 0412576805 |
Internformat
MARC
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| 100 | 1 | |a Filter, Wolfgang |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Integration theory |c W. Filter and K. Weber |
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| 264 | 1 | |a London [u.a.] |b Chapman & Hall |c 1997 | |
| 300 | |a XII, 294 S. | ||
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| 650 | 4 | |a Functions of real variables | |
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| 650 | 4 | |a Measure theory | |
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Datensatz im Suchindex
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| adam_text | Titel: Integration theory
Autor: Filter, Wolfgang
Jahr: 1997
Contents Preface vii Introduction ix 1 Preliminaries 1 2 Function spaces and functionals 9 2.1 Ordered sets and lattices 9 2.2 The spaces K x and ffi* 17 2.3 Vector lattices of functions 23 2.4 Functionals 30 2.5 Daniell spaces 46 3 Extension of Danieli spaces 49 3.1 Upper functions 50 3.2 Lower functions 53 3.3 The closure of ( X , £, £) 55 3.4 Convergence theorems for ( X, £(£), i) 62 3.5 Examples 69 3.6 Null functions, null sets and integrability 75 3.7 Examples 86 3.8 The induction principle 88 3.9 Functionals on K x 91 3.10 Summary 98 4 Measure and integral 101 4.1 Extensions of positive measure spaces 102 4.2 Examples 120 4.3 Locally integrable functions 124
vi Contents 4.4 ^-measurable functions 128 4.5 Product measures and Fubini’s theorem 139 5 Measures on Hausdorff spaces 159 5.1 Regular measures 159 5.2 Measures on metric and locally compact spaces 176 5.3 The congruence invariance of the n-dimensional Lebesgue measure 188 6 £ p -spaces 195 6.1 The structure of £ p -spaces 195 6.2 Uniform integrability 209 7 Vector lattices, £ p -spaces 221 7.1 Vector lattices 221 7.2 L p -spaces 235 8 Spaces of measures 241 8.1 The vector lattice structure and Hahn’s theorem 241 8.2 Absolute continuity and the Radon-Nikodym theorem 255 9 Elements of the theory of real-valued functions on R 263 9.1 Functions of locally finite variation 263 9.2 Absolutely continuous functions 268 Symbol index 283 Subject index 287
|
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| dewey-sort | 3515 242 |
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| discipline | Mathematik |
| edition | 1. ed. |
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| id | DE-604.BV011506202 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:10:55Z |
| institution | BVB |
| isbn | 0412576805 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007743172 |
| oclc_num | 37661439 |
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| physical | XII, 294 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Chapman & Hall |
| record_format | marc |
| series2 | Chapman & Hall mathematics series |
| spelling | Filter, Wolfgang Verfasser aut Integration theory W. Filter and K. Weber 1. ed. London [u.a.] Chapman & Hall 1997 XII, 294 S. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall mathematics series Functions of real variables Integrals, Generalized Measure theory Integration Mathematik (DE-588)4072852-3 gnd rswk-swf Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Integrationstheorie (DE-588)4138369-2 s DE-604 Integration Mathematik (DE-588)4072852-3 s Weber, Karl Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007743172&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Filter, Wolfgang Weber, Karl Integration theory Functions of real variables Integrals, Generalized Measure theory Integration Mathematik (DE-588)4072852-3 gnd Integrationstheorie (DE-588)4138369-2 gnd |
| subject_GND | (DE-588)4072852-3 (DE-588)4138369-2 |
| title | Integration theory |
| title_auth | Integration theory |
| title_exact_search | Integration theory |
| title_full | Integration theory W. Filter and K. Weber |
| title_fullStr | Integration theory W. Filter and K. Weber |
| title_full_unstemmed | Integration theory W. Filter and K. Weber |
| title_short | Integration theory |
| title_sort | integration theory |
| topic | Functions of real variables Integrals, Generalized Measure theory Integration Mathematik (DE-588)4072852-3 gnd Integrationstheorie (DE-588)4138369-2 gnd |
| topic_facet | Functions of real variables Integrals, Generalized Measure theory Integration Mathematik Integrationstheorie |
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