Radon measures on arbitrary topological spaces and cylindrical measures:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London, [u.a.]
Oxford University Press
1973
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| Series: | Tata Institute of Fundamental Research <Bombay>: Tata Institute of Fundamental Research studies in mathematics
6 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xii, 393 Seiten Illustrationen |
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Record in the Search Index
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| adam_text |
CONTENTS
Introduction . v
* Remeeciements . vii
PART I
Summary of Chapter I . 3
Chapter I. Radon Measures: Main Properties and Operations
1. Preliminaries . 7
2. Definition of Radon measure on general topological
spaces . 12
3. Induced measures . 20
4. Product of a measure by a locally integrable
function 23
5. Measurable mappings and image measures . . 25
6. Other properties of Radon measures . 40
7. Real and complex measures . . . .53
8. Different ways of defining Radon measures . . 58
9. Tensor product of measures . 63
10. Projective limit of measures . 74
11. Non Hausdorff spaces . 82
Summary of Chapter II . . . . . .89
Chapter II. Polish, Lusin, Suslin and Radon Spaces
1. Definitions and topological properties . 92
2. Examples of Lusin spaces . . . .112
3. Radon spaces . . . . . .117
4. Lifting of Ln to J2?" 130
5. Spaces of regulated functions . . . .136
Terminological Index to Part I . . . . • 144
x contents
References . . . . . . . . .146
PART II
Introduction to Part II . . . . . .151
Summary of Chapter I . . . . . . .152
Chapter I. Equivalent Topologies
1. Equivalent measures . . . . .153
2. Equivalent topologies . . . . .155
3. A Borel graph theorem . . . . .160
4. Equivalence of the strong and weak topologies . 161
5. Equivalence of the strong topology with coarser
topologies . . . . . . .166
Summary of Chapter II . . . . . . .171
Chapter II. Cylindrical Measures
1. Definition of cylindrical measures . . .172
2. Operations with cylindrical measures . . .180
3. Concentrations . . . . . . .188
Summary of Chapter III 206
Chapter III. Cylindrical Measures and Hilbert Sohmidt
Operators
1. Hilbert Schmidt operators . 207
2. The main lemma 212
3. The theorem of Sazonov . . . . .214
Summary of Chapter IV . . . . . .218
CONTENTS Xi
Chapter IV. Cylindrical Measures and Nuclear Spaces
1. Nuclear operators . . . . . .219
2. Nuclear spaces . 226
3. The theorem of Minlos 233
4. The theorem of Sazonov Badrikian . . . 237
Summary of Chapter V . 242
Chapter V. Cylindrical Measures and Probability theory
1. Basic concepts of probability theory . . . 244
2. Randon functions . 254
3. Examples and applications . 269
4. An analogue of Prokhorov's theorem for random
variables with values in a Suslin space . . . 288
5. Categories of random functions . 305
Summary of Chapter VI . 324
Chapter VI. Gauss Measures
1. The definition of Gauss measures . . . 325
2. The Hilbert subspaces of a locally convex space . 330
3. The converse of the theorems of Sazonov and Minlos 341
4. The analogue of Sazonov's theorem for lp spaces
(0 p + oo) and applications . . . 347
5. An application to Brownian motion . . .350
Summary of Appendix . 368
Appendix. Complements on Narrow Convergence
1. Narrow convergence on an arbitrary topological
space . 369
2. Riemann integrable functions . 374
t
Xii CONTENTS
3. A compactness criterion for the narrow topology . 379
4. A theorem of Paul LeVy 382
5. The space of finite measures on a Suslin space . 385
Terminological Index to Part II . . . . . 390
References . 392 |
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| genre_facet | Zylindrisches Maß |
| id | DE-604.BV002759772 |
| illustrated | Illustrated |
| indexdate | 2025-02-11T09:01:46Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001764096 |
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| physical | xii, 393 Seiten Illustrationen |
| publishDate | 1973 |
| publishDateSearch | 1973 |
| publishDateSort | 1973 |
| publisher | Oxford University Press |
| record_format | marc |
| series | Tata Institute of Fundamental Research <Bombay>: Tata Institute of Fundamental Research studies in mathematics |
| series2 | Tata Institute of Fundamental Research <Bombay>: Tata Institute of Fundamental Research studies in mathematics |
| spelling | Schwartz, Laurent 1915-2002 (DE-588)118795694 aut Radon measures on arbitrary topological spaces and cylindrical measures Laurent Schwartz London, [u.a.] Oxford University Press 1973 xii, 393 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Tata Institute of Fundamental Research <Bombay>: Tata Institute of Fundamental Research studies in mathematics 6 Rotationssymmetrisches Werkstück (DE-588)4178510-1 gnd rswk-swf Radon-Maß (DE-588)4242168-8 gnd rswk-swf Rotationssymmetrisches Werkstück (DE-588)4178510-1 s DE-604 Radon-Maß (DE-588)4242168-8 s Tata Institute of Fundamental Research <Bombay>: Tata Institute of Fundamental Research studies in mathematics 6 (DE-604)BV004244858 6 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001764096&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schwartz, Laurent 1915-2002 Radon measures on arbitrary topological spaces and cylindrical measures Tata Institute of Fundamental Research <Bombay>: Tata Institute of Fundamental Research studies in mathematics Rotationssymmetrisches Werkstück (DE-588)4178510-1 gnd Radon-Maß (DE-588)4242168-8 gnd |
| subject_GND | (DE-588)4178510-1 (DE-588)4242168-8 |
| title | Radon measures on arbitrary topological spaces and cylindrical measures |
| title_auth | Radon measures on arbitrary topological spaces and cylindrical measures |
| title_exact_search | Radon measures on arbitrary topological spaces and cylindrical measures |
| title_full | Radon measures on arbitrary topological spaces and cylindrical measures Laurent Schwartz |
| title_fullStr | Radon measures on arbitrary topological spaces and cylindrical measures Laurent Schwartz |
| title_full_unstemmed | Radon measures on arbitrary topological spaces and cylindrical measures Laurent Schwartz |
| title_short | Radon measures on arbitrary topological spaces and cylindrical measures |
| title_sort | radon measures on arbitrary topological spaces and cylindrical measures |
| topic | Rotationssymmetrisches Werkstück (DE-588)4178510-1 gnd Radon-Maß (DE-588)4242168-8 gnd |
| topic_facet | Rotationssymmetrisches Werkstück Radon-Maß |
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| volume_link | (DE-604)BV004244858 |
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