Finitely additive measures and relaxations of extremal problems:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York [u.a.]
Consultants Bureau
1996
|
| Schriftenreihe: | Monographs in contemporary mathematics
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007684813&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Aus dem Russ. übers. |
| Umfang: | XI, 244 S. |
| ISBN: | 0306110385 |
Internformat
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Datensatz im Suchindex
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| adam_text | FINITELY ADDITIVE MEASURES AND RELAXATIONS OF EXTREMAL PROBLEMS A. G.
CHENTSOV MATHEMATICS AND MECHANICS INSTITUTE URALS DIVISION OF THE
RUSSIAN ACADEMY OF SCIENCES EKATERINBURG, RUSSIA TRANSLATED FROM RUSSIAN
BY A. V. LUTSUK CONSULTANTS BUREAU * NEW YORK, LONDON, AND MOSCOW
CONTENTS CHAPTER 1. RELAXATIONS OF EXTREMAL PROBLEMS 1 1.1. INTRODUCTION
1 1.2. RELAXATIONS OF INTEGRAL CONSTRAINTS 2 1.3. CONSTRAINTS IMPOSED ON
THE VECTOR INTEGRAND OF A CONTROL ... 7 1.4. ASYMPTOTIC EFFECTS IN A
CONE OPTIMIZATION PROBLEM (AN EX- AMPLE) 13 CHAPTER 2. COMPACTIFICATORS
IN EXTREMAL PROBLEMS 19 2.1. INTRODUCTION 19 2.2. SOME NOTIONS FROM
TOPOLOGY 20 2.3. COMPACTIFICATOR- OF AN EXTREMAL PROBLEM WITH
CONSTRAINTS OF ASYMPTOTIC CHARACTER 26 2.4. SOME NOTIONS OF SET THEORY.
PRODUCTS OF TOPOLOGICAL SPACES . 33 2.5. THE PROBLEM OF ASYMPTOTIC
OPTIMIZATION IN APREORDERED SPACE AND ITS EXTENSION ; 39 2.6. EXTENSION
OF THE CONE OPTIMIZATION PROBLEM I 45 CHAPTER 3. FINITELY ADDITIVE
MEASURES ON A SEMIALGEBRA OF SETS 55 3.1. INTRODUCTION 55 3.2.
SEMIALGEBRAS AND ALGEBRAS OF SETS 57 3.3. FINITELY ADDITIVE MEASURES . .
. /X 59 3.4. MEASURES AND INTEGRAL REPRESENTATION OF LINEAR FUNCTIONALS
. . 65 3.5. COMPACTIFICATION IN THE CLASS OF TWO-VALUED MEASURES 71 3.6.
EXTENSION OF THE CONE OPTIMIZATION PROBLEM IN THE CLASS OF TWO-VALUED
MEASURES 72 IX X CONTENTS CHAPTER 4. FINITELY ADDITIVE MEASURES AND
INDEFINITE INTE- GRALS 77 4.1. INTRODUCTION 77 4.2. WEAKLY ABSOLUTELY
CONTINUOUS FINITELY ADDITIVE MEASURES . . 79 4.3. DENSITY PROPERTIES 83
4.4. EXAMPLES 89 CHAPTER 5. ADMISSIBLE SETS AND THEIR RELAXATIONS 97
5.1. INTRODUCTION 97 5.2. ASYMPTOTICS OF PERTURBED CONSTRAINTS AND ITS
LIMIT REPRESEN- TATION (CASE OF POSITIVE MEASURES) 100 5.3. ASYMPTOTICS
OF PERTURBED CONSTRAINTS AND ITS LIMIT REPRESEN- TATION (CASE OF
ALTERNATING MEASURES) 104 5.4. STRONG BOUNDEDNESS CONDITIONS AND
RELAXATIONS OF ADMISSIBLE SETS. I 108 5.5. STRONG BOUNDEDNESS CONDITIONS
AND RELAXATIONS OF ADMISSIBLE SETS. II 113 CHAPTER 6. RELAXATIONS OF
ATTAINABLE SETS 121 6.1. INTRODUCTION 121 6.2. LIMIT REPRESENTATION OF
ATTAINABLE SETS 122 6.3. ASYMPTOTIC NONSENSITIVITY AND RELAXATIONS OF
ATTAINABLE SETS (CASE OF POSITIVE MEASURES) 125 6.4. ASYMPTOTIC
NONSENSITIVITY AND RELAXATIONS OF ATTAINABLE SETS (CASE OF ALTERNATING
MEASURES) 131 6.5. ATTAINABILITY DOMAINS OF CONTROLLABLE SYSTEMS AND
THEIR RE- LAXATIONS 135 CHAPTER 7. ASYMPTOTIC VALUES AND THEIR
GENERALIZED REP- RESENTATION 139 7.1. INTRODUCTION 139 7.2. EXAMPLE 140
7.3. GENERALIZED EXTREMAL PROBLEM AND ASYMPTOTIC VALUES 143 7.4. VALUE
ASYMPTOTICS FOR STRONGLY BOUNDED PROBLEMS 151 7.5. ON AN EXTREMAL
PROBLEM WITH INEQUALITY-TYPE CONSTRAINTS . . 159 CHAPTER 8. ASYMPTOTIC
EFFICIENCY 167 8.1. INTRODUCTION 167 8.2. GENERALIZED PROBLEM OF CONE
OPTIMIZATION. I 168 CONTENTS XI 8.3. GENERALIZED PROBLEM OF CONE
OPTIMIZATION. II 177 CHAPTER 9. ISSUES OF COMPUTATIONAL STABILITY 185
9.1. INTRODUCTION 185 9.2. CONSTRAINTS ON THE VECTOR INTEGRAND 186 9.3.
COMPUTATIONAL STABILITY 193 9.4. A PROBLEM OF THE EXTREMAL CHOICE OF
PROBABILITY DENSITY . . . 194 9.5. EXTENSION IN THE CLASS OF VECTOR
FINITELY ADDITIVE MEASURES . . 198 CONCLUSION 231 REFERENCES 235 INDEX
243
|
| any_adam_object | 1 |
| author | Čencov, Aleksandr Georgievič 1947- |
| author_GND | (DE-588)1055925732 |
| author_facet | Čencov, Aleksandr Georgievič 1947- |
| author_role | aut |
| author_sort | Čencov, Aleksandr Georgievič 1947- |
| author_variant | a g č ag agč |
| building | Verbundindex |
| bvnumber | BV011428481 |
| classification_rvk | SK 430 |
| ctrlnum | (OCoLC)833038693 (DE-599)BVBBV011428481 |
| dewey-full | 515.42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.42 |
| dewey-search | 515.42 |
| dewey-sort | 3515.42 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011428481 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:12:16Z |
| institution | BVB |
| isbn | 0306110385 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007684813 |
| oclc_num | 833038693 |
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| owner | DE-12 DE-703 DE-83 |
| owner_facet | DE-12 DE-703 DE-83 |
| physical | XI, 244 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Consultants Bureau |
| record_format | marc |
| series2 | Monographs in contemporary mathematics |
| spellingShingle | Čencov, Aleksandr Georgievič 1947- Finitely additive measures and relaxations of extremal problems Endlich additives Maß (DE-588)4401247-0 gnd Extremwert (DE-588)4137272-4 gnd |
| subject_GND | (DE-588)4401247-0 (DE-588)4137272-4 |
| title | Finitely additive measures and relaxations of extremal problems |
| title_alt | Konečno-additivnye mery i relaksacii ėkstremal'nych zadač |
| title_auth | Finitely additive measures and relaxations of extremal problems |
| title_exact_search | Finitely additive measures and relaxations of extremal problems |
| title_full | Finitely additive measures and relaxations of extremal problems A. G. Chentsov |
| title_fullStr | Finitely additive measures and relaxations of extremal problems A. G. Chentsov |
| title_full_unstemmed | Finitely additive measures and relaxations of extremal problems A. G. Chentsov |
| title_short | Finitely additive measures and relaxations of extremal problems |
| title_sort | finitely additive measures and relaxations of extremal problems |
| topic | Endlich additives Maß (DE-588)4401247-0 gnd Extremwert (DE-588)4137272-4 gnd |
| topic_facet | Endlich additives Maß Extremwert |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007684813&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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