Measures on infinite dimensional spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore, [u.a.]
World Scientific
[1985]
|
| Series: | Series in pure mathematics
Volume 5 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | viii, 256 Seiten Illustrationen |
| ISBN: | 9971978520 |
Staff View
MARC
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| 245 | 1 | 0 | |a Measures on infinite dimensional spaces |c Y Yamasaki |
| 264 | 1 | |a Singapore, [u.a.] |b World Scientific |c [1985] | |
| 264 | 4 | |c © 1985 | |
| 300 | |a viii, 256 Seiten |b Illustrationen | ||
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| 490 | 1 | |a Series in pure mathematics |v Volume 5 | |
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Record in the Search Index
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CONTENTS
PART A: EXTENDABILITY OF A FAMILY OF MEASURES TO A o ADDITIVE
MEASURE
(Kolmogorov Bochner Minlos Theory)
Introduction 3
Chapter 1. Preliminary discussions 4
§ 1. Explanation of the problem 4
§2. Tychonov's theorem 6
§3. Hopf s theorem 9
Chapter 2. Direct product and projective limit 14
§4. Measurable spaces, their product and limit 14
§5. Extension problems and counter examples 17
§6. Extension theorem for direct product 22
§7. Extension theorem for projective limit 26
§8. Non countable direct product and projective limit 30
§9. Compact regular measurable space 35
§10. Borel field 38
§11. Baire field 42
§ 12. Product measure 46
§ 13. Suslin set, Luzin set 50
§ 14. Standard measurable space 56
Chapter 3. Measures on vector spaces 63
§15. Explanation of the problem 63
§ 16. Relation with Bochner's theorem 68
§ 17. Minlos' theorem 72
§ 18. Sazonov topology 77
§19. Supplementary results 81
§20. Nuclear space 85
§21. Heredity 89
§22. Dual space 95
Appendix. Definition of nuclearity without using Hilbertian semi norms 98
Note 106
PART B: INVARIANCE AND QUASI INVARIANCE OF MEASURES ON
INFINITE DIMENSIONAL SPACES
Introduction Ill
Chapter 1. Invariant measure on a group 113
§ 1. Measurable group, invariant and quasi invariant measure 113
viii
§2. Haar measure on a locally compact group 118
§3. Haar measure on a thick group 125
§4. Weil topology 133
§5. Case of a vector space 138
Chapter 2. Gaussian measures and related problems 144
§6. Quasi invariance and ergodicity , 144
§7. Absolute continuity of projective limit measures 147
§8. Gaussian measures 151
§9. E' quasi invariance and E' ergodicity 154
§10. Mutual equivalence 160
§11. Rotationally invariant measures 163
§12. Representation of L2(m) 167
Chapter 3. The set V^ of all quasi invariant translations 174
§ 13. Convolution of measures 174
§ 14. Linearization of a topology on a vector space 175
§15. Characteristic topology 177
§16. Evaluation of Yn in terms of t,, 181
§ 17. Some applications 184
§18. Kakutani topology 189
§ 19. Evaluation of Y^ in terms of Kakutani topology 195
Chapter 4. Product measures on R" 202
§20. Product of one dimensional probability measures 202
§21. Stationary product measures 208
§22. Gaussian measures and stationary products 212
§23. Estimation of Y^ and R^ 216
§24. Non stationary product measures 219
§25. (K2 ) quasi invariance 222
Chapter 5. Ro invariant measures on R°° 227
§26. Infinite dimensional Lebesgue measure 227
§27. IRj^ ergodicity and mutual equivalence 230
§28. Equivalent probability measure of product type 233
§29. The converse problem of §28 235
§30. Linear transformation of /u^ 240
§31. Rotational invariance and ergodicity 244
§32. Invariance under homotheties 247
Note 251
Index 255 |
| any_adam_object | 1 |
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| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000554594 |
| illustrated | Illustrated |
| indexdate | 2025-03-26T17:00:39Z |
| institution | BVB |
| isbn | 9971978520 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000341206 |
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| physical | viii, 256 Seiten Illustrationen |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | World Scientific |
| record_format | marc |
| series | Series in pure mathematics |
| series2 | Series in pure mathematics |
| spelling | Yamasaki, Yasuo 1934- (DE-588)1203574819 aut Measures on infinite dimensional spaces Y Yamasaki Singapore, [u.a.] World Scientific [1985] © 1985 viii, 256 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Series in pure mathematics Volume 5 Generalized spaces Measure theory Unendlichdimensionaler Raum (DE-588)4207852-0 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Maßtheorie (DE-588)4074626-4 s Unendlichdimensionaler Raum (DE-588)4207852-0 s DE-604 Series in pure mathematics Volume 5 (DE-604)BV000016845 5 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000341206&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yamasaki, Yasuo 1934- Measures on infinite dimensional spaces Series in pure mathematics Generalized spaces Measure theory Unendlichdimensionaler Raum (DE-588)4207852-0 gnd Maßtheorie (DE-588)4074626-4 gnd |
| subject_GND | (DE-588)4207852-0 (DE-588)4074626-4 |
| title | Measures on infinite dimensional spaces |
| title_auth | Measures on infinite dimensional spaces |
| title_exact_search | Measures on infinite dimensional spaces |
| title_full | Measures on infinite dimensional spaces Y Yamasaki |
| title_fullStr | Measures on infinite dimensional spaces Y Yamasaki |
| title_full_unstemmed | Measures on infinite dimensional spaces Y Yamasaki |
| title_short | Measures on infinite dimensional spaces |
| title_sort | measures on infinite dimensional spaces |
| topic | Generalized spaces Measure theory Unendlichdimensionaler Raum (DE-588)4207852-0 gnd Maßtheorie (DE-588)4074626-4 gnd |
| topic_facet | Generalized spaces Measure theory Unendlichdimensionaler Raum Maßtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000341206&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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