A course on Borel sets:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
New York [u.a.]
Springer
1998
|
| Series: | Graduate texts in mathematics
180 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 261 S. graph. Darst. |
| ISBN: | 0387984127 |
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MARC
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Record in the Search Index
| _version_ | 1804126655830032384 |
|---|---|
| adam_text | Contents
Acknowledgments vii
Introduction xi
About This Book xv
1 Cardinal and Ordinal Numbers 1
1.1 Countable Sets 1
1.2 Order of Infinity 4
1.3 The Axiom of Choice 7
1.4 More on Equinumerosity 11
1.5 Arithmetic of Cardinal Numbers 13
1.6 Well Ordered Sets 15
1.7 Transfinite Induction 18
1.8 Ordinal Numbers 21
1.9 Alephs 24
1.10 Trees 26
1.11 Induction on Trees 29
1.12 The Souslin Operation 31
1.13 Idempotence of the Souslin Operation 34
2 Topological Preliminaries 39
2.1 Metric Spaces 39
2.2 Polish Spaces 52
2.3 Compact Metric Spaces 57
2.4 More Examples 63
x Contents
2.5 The Baire Category Theorem 69
2.6 Transfer Theorems 74
3 Standard Borel Spaces 81
3.1 Measurable Sets and Functions 81
3.2 Borel Generated Topologies 91
3.3 The Borel Isomorphism Theorem 94
3.4 Measures 100
3.5 Category 107
3.6 Borel Pointclasses 115
4 Analytic and Coanalytic Sets 127
4.1 Projective Sets 127
4.2 £} and 11} Complete Sets 135
4.3 Regularity Properties 141
4.4 The First Separation Theorem 147
4.5 One to One Borel Functions 150
4.6 The Generalized First Separation Theorem 155
4.7 Borel Sets with Compact Sections 157
4.8 Polish Groups 160
4.9 Reduction Theorems 164
4.10 Choquet Capacitability Theorem 172
4.11 The Second Separation Theorem 175
4.12 Countable to One Borel Functions 178
5 Selection and Uniformization Theorems 183
5.1 Preliminaries 184
5.2 Kuratowski and Ryll Nardzewski s Theorem 189
5.3 Dubins Savage Selection Theorems 194
5.4 Partitions into Closed Sets 195
5.5 Von Neumann s Theorem 198
5.6 A Selection Theorem for Group Actions 200
5.7 Borel Sets with Small Sections 204
5.8 Borel Sets with Large Sections 206
5.9 Partitions into G6 Sets 212
5.10 Reflection Phenomenon 216
5.11 Complementation in Borel Structures 218
5.12 Borel Sets with a Compact Sections 219
5.13 Topological Vaught Conjecture 227
5.14 Uniformizing Coanalytic Sets 236
References 241
Glossary 251
Index 253
|
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| id | DE-604.BV012058164 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:20:55Z |
| institution | BVB |
| isbn | 0387984127 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008161200 |
| oclc_num | 833239815 |
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| physical | XVI, 261 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Srivastava, Sashi Mohan Verfasser aut A course on Borel sets S. M. Srivastava New York [u.a.] Springer 1998 XVI, 261 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 180 Borel-Menge (DE-588)4146323-7 gnd rswk-swf Borel-Menge (DE-588)4146323-7 s DE-604 Graduate texts in mathematics 180 (DE-604)BV000000067 180 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008161200&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Srivastava, Sashi Mohan A course on Borel sets Graduate texts in mathematics Borel-Menge (DE-588)4146323-7 gnd |
| subject_GND | (DE-588)4146323-7 |
| title | A course on Borel sets |
| title_auth | A course on Borel sets |
| title_exact_search | A course on Borel sets |
| title_full | A course on Borel sets S. M. Srivastava |
| title_fullStr | A course on Borel sets S. M. Srivastava |
| title_full_unstemmed | A course on Borel sets S. M. Srivastava |
| title_short | A course on Borel sets |
| title_sort | a course on borel sets |
| topic | Borel-Menge (DE-588)4146323-7 gnd |
| topic_facet | Borel-Menge |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008161200&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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