Nonstandard analysis and vector lattices:
Saved in:
| Format: | Book |
|---|---|
| Language: | English Russian |
| Published: |
Dordrecht [u.a.]
Kluwer
2000
|
| Series: | Mathematics and its applications
525 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 307 S. |
| ISBN: | 0792366190 |
Staff View
MARC
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Record in the Search Index
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| adam_text | NONSTANDARD ANALYSIS AND VECTOR LATTICES EDITED BY S.S. KUTATELADZE
SOBOLEV INSTITUTE OF MATHEMATICS, SIBERIAN DIVISION OFTHE RUSSIAN
ACADEMY OF SCIENCES, NOVOSIBIRSK, RUSSIA KLUWER ACADEMIC PUBLISHERS
DORDRECHT / BOSTON / LONDON CONTENTS FOREWORD IX CHAPTER 1. NONSTANDARD
METHODS AND KANTOROVICH SPACES (A. G. KUSRAEV AND S. S. KUTATELADZE) 1
§1.1. ZERMELO-PRAENKEL SET THEORY 5 § 1.2. BOOLEAN VALUED SET THEORY 7 §
1.3. INTERNAL AND EXTERNAL SET THEORIES 12 § 1.4. RELATIVE INTERNAL SET
THEORY 18 § 1.5. KANTOROVICH SPACES 23 § 1.6. REALS INSIDE BOOLEAN
VALUED MODELS 26 § 1.7. PUNCTIONAL CALCULUS IN KANTOROVICH SPACES 30 §
1.8. LATTICE NORMED SPACES 34 § 1.9. NONSTANDARD HULLS 40 § 1.10. THE
LOEB MEASURE 44 § 1.11. BOOLEAN VALUED MODELING IN A NONSTANDARD
UNIVERSE 48 § 1.12. INFINITESIMAL MODELING IN A BOOLEAN VALUED UNIVERSE
53 § 1.13. EXTENSION AND DECOMPOSITION OF POSITIVE OPERATORS 57 § 1.14.
FRAGMENTS OF POSITIVE OPERATORS 61 § 1.15. ORDER CONTINUOUS OPERATORS 65
§ 1.16. CYCLICALLY COMPACT OPERATORS 69 REFERENCES 73 VI CONTENTS
CHAPTER 2. FUNCTIONAL REPRESENTATION OF A BOOLEAN VALUED UNIVERSE (A. E.
GUTMAN AND G. A. LOSENKOV) 81 § 2.1. PRELIMINARIES 83 § 2.2. THE CONCEPT
OF CONTINUOUS BUENDLE 89 § 2.3. A CONTINUOUS POLYVERSE 92 § 2.4.
FUNCTIONAL REPRESENTATION 100 REFERENCES 104 CHAPTER 3. DUAL BANACH
BUNDLES (A. E. GUTMAN AND A. V. KOPTEV) 105 § 3.1. AUXILIARY RESULTS 109
§ 3.2. HOMOMORPHISMS OF BANACH BUNDLES 119 § 3.3. AN OPERATOR BUENDLE 130
§ 3.4. THE DUAL OF A BANACH BUENDLE 138 § 3.5. WEAKLY CONTINUOUS SECTIONS
150 REFERENCES 158 CHAPTER 4. INFINITESIMALS IN VECTOR LATTICES (E. YU.
EMEL YANOV) 161 § 4.0. PRELIMINARIES 164 § 4.1. SATURATED SETS OF
INDIVISIBLES 172 § 4.2. REPRESENTATION OF ARCHIMEDEAN VECTOR LATTICES
178 § 4.3. ORDER, RELATIVE UNIFORM CONVERGENCE, AND THE ARCHIMEDES
PRINCIPLE 184 § 4.4. CONDITIONAL COMPLETION AND ATOMICITY 189 § 4.5.
NORMED VECTOR LATTICES 19 4 § 4.6. LINEAR OPERATORS BETWEEN VECTOR
LATTICES 198 § 4.7. ^-INVARIANT HOMOMORPHISMS 201 § 4.8. ORDER HULLS OF
VECTOR LATTICES 206 § 4.9. REGULAER HULLS OF VECTOR LATTICES 211 § 4.10.
ORDER AND REGULAER HULLS OF LATTICE NORMED SPACES 214 § 4.11. ASSOCIATED
BANACH-KANTOROVICH SPACES 220 REFERENCES 228 CONTENTS VII CHAPTER 5.
VECTOR MEASURES AND DOMINATED MAPPINGS (A. G. KUSRAEV AND S. A.
MALYUGIN) 231 § 5.1. VECTOR MEASURES 234 § 5.2. QUASI-RADON AND
QUASIREGULAR MEASURES 236 § 5.3. INTEGRAL REPRESENTATIONS AND EXTENSION
OF MEASURES 241 § 5.4. THE FUBINI THEOREM 247 § 5.5. THE HAUSDORFF
MOMENT PROBLEM 256 § 5.6. THE HAMBURGER MOMENT PROBLEM 260 § 5.7. THE
HAMBURGER MOMENT PROBLEM FOR DOMINANT MOMENT SEQUENCES 272 § 5.8.
DOMINATED MAPPINGS 278 § 5.9. THE BOCHNER THEOREM FOR DOMINATED MAPPINGS
286 § 5.10. CONVOLUTION 29 0 §5.11. BOOLEAN VALUED INTERPRETATION OF THE
WIENER LEMMA 294 REFERENCES 296 NOTATION INDEX 300 SUBJECT INDEX 303
|
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| indexdate | 2024-07-09T18:53:54Z |
| institution | BVB |
| isbn | 0792366190 |
| language | English Russian |
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| physical | XII, 307 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Nonstandard analysis and vector lattices ed. by S. S. Kutateladze Dordrecht [u.a.] Kluwer 2000 XII, 307 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 525 Nonstandard mathematical analysis Vector lattices, Archimedian Nonstandard-Analysis (DE-588)4137021-1 gnd rswk-swf Vektorverband (DE-588)4187471-7 gnd rswk-swf Nonstandard-Analysis (DE-588)4137021-1 s Vektorverband (DE-588)4187471-7 s DE-604 Kutateladze, Semen S. 1945- Sonstige (DE-588)123299268 oth Mathematics and its applications 525 (DE-604)BV008163334 525 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009504151&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nonstandard analysis and vector lattices Mathematics and its applications Nonstandard mathematical analysis Vector lattices, Archimedian Nonstandard-Analysis (DE-588)4137021-1 gnd Vektorverband (DE-588)4187471-7 gnd |
| subject_GND | (DE-588)4137021-1 (DE-588)4187471-7 |
| title | Nonstandard analysis and vector lattices |
| title_auth | Nonstandard analysis and vector lattices |
| title_exact_search | Nonstandard analysis and vector lattices |
| title_full | Nonstandard analysis and vector lattices ed. by S. S. Kutateladze |
| title_fullStr | Nonstandard analysis and vector lattices ed. by S. S. Kutateladze |
| title_full_unstemmed | Nonstandard analysis and vector lattices ed. by S. S. Kutateladze |
| title_short | Nonstandard analysis and vector lattices |
| title_sort | nonstandard analysis and vector lattices |
| topic | Nonstandard mathematical analysis Vector lattices, Archimedian Nonstandard-Analysis (DE-588)4137021-1 gnd Vektorverband (DE-588)4187471-7 gnd |
| topic_facet | Nonstandard mathematical analysis Vector lattices, Archimedian Nonstandard-Analysis Vektorverband |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009504151&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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