Topological measures and weighted radon measures:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Alpha Science International Ltd.
2008
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 263 S. |
| ISBN: | 9781842652831 |
Staff View
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| 245 | 1 | 0 | |a Topological measures and weighted radon measures |c D. P. L. Castrigiano ; W. Rölcke |
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Record in the Search Index
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| adam_text | Contents
Preface.................................... v
1 Abstract measures and densities 1
1.1 Outer measure and upper integral ............... 1
1.2 Essential outer measure and essential upper integral..... 11
1.3 Restriction of a measure to a sub-cr-algebra.......... 23
1.4 Densities.............................. 25
1.5 Point-finite, star-countable, and independent families..... 32
2 Measures on topological spaces 35
2.1 Regularity properties of topological measures......... 38
2.1.1 Definitions and basic results............... 38
2.1.2 Implications of topological properties.......... 51
2.1.3 crcc and Lc property................... 74
2.1.4 Borel regularity of the essential outer measure .... 76
2.2 Some results on the support................... 80
2.3 Radon measures ......................... 89
2.4 Locally finite tight measures................... 97
2.4.1 Equivalence of locally finite tight measures and Radon
measures ......................... 97
2.4.2 Tight Radon measures.................. 103
2.4.3 Regularity properties of integrals............ 107
2.5 Set functions on the compact sets and outer measures with
regularity properties....................... 108
2.6 Two special types of topological measure spaces........ 113
2.7 Riesz representation theorem and infinite topological product
of probability measures on compact spaces........... 125
x Contents
3 Regularity properties of weighted Radon measures 136
3.1 Radon measure r associated to v................ 137
3.2 Tightness for v.......................... 148
3.3 Inner regularity for v....................... 150
3.4 Outer regularity for v and v î ................. 154
3.5 Rm property for i/|B and v................... 158
3.6 Weight functions of special type................. 160
3.7 Differences, sums, suprema, and infima of weight functions . . 166
3.8 Hausdorff spaces with additional properties.......... 168
3.9 me property for ß and v..................... 172
4 crcc and Lc spaces 176
4.1 tree property and mappings...................177
4.2 Locally compact rcc spaces...................179
4.3 ace coverings and products of rcc spaces............182
4.4 ace, Lc, paracompact, locally compact paracompact.....184
4.5 Generalized ordered spaces...................188
4.6 P-spaces and other special crcc spaces .............189
4.7 Examples.............................194
4.7.1 Locally compact spaces.................194
4.7.2 Non-locally compact spaces...............203
5 Counterexamples 207
5.1 crcc spaces.............................208
5.2 Non-crcc spaces..........................219
5.3 A topological measure space by Premlin............239
5.4 Thomas plank-like non-crcc spaces ...............245
Bibliography 249
Notation Index 254
Subject Index 256
|
| any_adam_object | 1 |
| author | Castrigiano, Domenico P. L. 1946- Roelcke, Walter 1928-2005 |
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| ctrlnum | (OCoLC)227980646 (DE-599)BSZ278795668 |
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| id | DE-604.BV035504178 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:39:06Z |
| institution | BVB |
| isbn | 9781842652831 |
| language | English |
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| owner_facet | DE-91G DE-BY-TUM DE-11 |
| physical | X, 263 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Alpha Science International Ltd. |
| record_format | marc |
| spelling | Castrigiano, Domenico P. L. 1946- Verfasser (DE-588)109586239 aut Topological measures and weighted radon measures D. P. L. Castrigiano ; W. Rölcke Oxford Alpha Science International Ltd. 2008 X, 263 S. txt rdacontent n rdamedia nc rdacarrier Measure theory Radon measures Topology Radon-Maß (DE-588)4242168-8 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Maßtheorie (DE-588)4074626-4 s Topologie (DE-588)4060425-1 s DE-604 Radon-Maß (DE-588)4242168-8 s Roelcke, Walter 1928-2005 Verfasser (DE-588)101716309X aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017560350&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Castrigiano, Domenico P. L. 1946- Roelcke, Walter 1928-2005 Topological measures and weighted radon measures Measure theory Radon measures Topology Radon-Maß (DE-588)4242168-8 gnd Topologie (DE-588)4060425-1 gnd Maßtheorie (DE-588)4074626-4 gnd |
| subject_GND | (DE-588)4242168-8 (DE-588)4060425-1 (DE-588)4074626-4 |
| title | Topological measures and weighted radon measures |
| title_auth | Topological measures and weighted radon measures |
| title_exact_search | Topological measures and weighted radon measures |
| title_full | Topological measures and weighted radon measures D. P. L. Castrigiano ; W. Rölcke |
| title_fullStr | Topological measures and weighted radon measures D. P. L. Castrigiano ; W. Rölcke |
| title_full_unstemmed | Topological measures and weighted radon measures D. P. L. Castrigiano ; W. Rölcke |
| title_short | Topological measures and weighted radon measures |
| title_sort | topological measures and weighted radon measures |
| topic | Measure theory Radon measures Topology Radon-Maß (DE-588)4242168-8 gnd Topologie (DE-588)4060425-1 gnd Maßtheorie (DE-588)4074626-4 gnd |
| topic_facet | Measure theory Radon measures Topology Radon-Maß Topologie Maßtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017560350&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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