Integration - a functional approach
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
1998
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| Schriftenreihe: | Birkhäuser advanced texts
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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MARC
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Datensatz im Suchindex
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| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040020261038 |
| DE-BY-UBM_katkey | 2671859 |
| DE-BY-UBM_media_number | 99992441742 |
| _version_ | 1823052339131449344 |
| adam_text | Contents
Preface vii
Chapter I Review 1
1.1 Introduction 1
1.2 Notation 3
1.3 The Theorem of Stone Weierstrafi 8
1.4 The Riemann Integral 17
1.5 An Integrability Criterion 21
1.6 The Permanence Properties 23
1.7 Seminorms 28
Chapter II Extension of the Integral 31
II. 1 E additivity 33
11.2 Elementary Integrals 35
11.3 The Daniell Mean 42
11.4 Negligible Functions and Sets 48
11.5 Integrable Functions 52
11.6 Extending the Integral 58
11.7 Integrable Sets 61
11.8 Example of a Non Integrable Function 66
Chapter III Measurability 69
111.1 Littlewood s Principles 70
111.2 The Permanence Properties 73
111.3 The Integrability Criterion 75
111.4 Measurable Sets 81
111.5 Baire and Borel Functions 85
111.6 Further Properties of Daniell s Mean 92
111.7 The Procedures of Lebesgue and Carathedory 95
vi
Chapter IV The Classical Banach Spaces 101
IV.1 The p norms 102
IV.2 The CP spaces 105
IV.3 The LP spaces 108
IV.4 Linear Functionals 112
IV.5 The Dual of LP 118
IV.6 The Hilbert space L2 122
Chapter V Operations on Measures 125
V.I Products of Elementary Integrals 125
V.2 The Theorems of Fubini and Tonelli 130
V.3 An Application: Convolution 133
V.4 An Application: Marcinkiewicz Interpolation 134
V.5 Signed Measures 137
V.6 The Space of Measures 144
V.7 Measures with Densitites 151
V.8 The Radon Nikodym Theorem 154
V.9 An Application: Conditional Expectation 155
V.10 Differentiation 157
Appendix A Answers to Selected Problems 165
References 180
Index of Notations 181
Index 184
|
| any_adam_object | 1 |
| author | Bichteler, Klaus 1938- |
| author_GND | (DE-588)106060279 |
| author_facet | Bichteler, Klaus 1938- |
| author_role | aut |
| author_sort | Bichteler, Klaus 1938- |
| author_variant | k b kb |
| building | Verbundindex |
| bvnumber | BV011849152 |
| callnumber-first | Q - Science |
| callnumber-label | QA312 |
| callnumber-raw | QA312.B53 1998 |
| callnumber-search | QA312.B53 1998 |
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| callnumber-subject | QA - Mathematics |
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| classification_tum | MAT 280f |
| ctrlnum | (OCoLC)38910271 (DE-599)BVBBV011849152 |
| dewey-full | 515/.4321 515/.43 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.43 21 515/.43 |
| dewey-search | 515/.43 21 515/.43 |
| dewey-sort | 3515 243 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011849152 |
| illustrated | Not Illustrated |
| indexdate | 2025-02-03T16:44:36Z |
| institution | BVB |
| isbn | 3764359366 0817659366 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008003466 |
| oclc_num | 38910271 |
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| physical | VIII, 193 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Birkhäuser advanced texts |
| spellingShingle | Bichteler, Klaus 1938- Integration - a functional approach Integrals Measure theory Integrationstheorie (DE-588)4138369-2 gnd Integration Mathematik (DE-588)4072852-3 gnd Maßtheorie (DE-588)4074626-4 gnd Lebesgue-Integral (DE-588)4034949-4 gnd Riemannsches Integral (DE-588)4049996-0 gnd |
| subject_GND | (DE-588)4138369-2 (DE-588)4072852-3 (DE-588)4074626-4 (DE-588)4034949-4 (DE-588)4049996-0 |
| title | Integration - a functional approach |
| title_auth | Integration - a functional approach |
| title_exact_search | Integration - a functional approach |
| title_full | Integration - a functional approach Klaus Bichteler |
| title_fullStr | Integration - a functional approach Klaus Bichteler |
| title_full_unstemmed | Integration - a functional approach Klaus Bichteler |
| title_short | Integration - a functional approach |
| title_sort | integration a functional approach |
| topic | Integrals Measure theory Integrationstheorie (DE-588)4138369-2 gnd Integration Mathematik (DE-588)4072852-3 gnd Maßtheorie (DE-588)4074626-4 gnd Lebesgue-Integral (DE-588)4034949-4 gnd Riemannsches Integral (DE-588)4049996-0 gnd |
| topic_facet | Integrals Measure theory Integrationstheorie Integration Mathematik Maßtheorie Lebesgue-Integral Riemannsches Integral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008003466&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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