Convex analysis and measurable multifunctions:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1977
|
| Series: | Lecture notes in mathematics
580 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 278 S. |
| ISBN: | 3540081445 0387081445 |
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MARC
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| 245 | 1 | 0 | |a Convex analysis and measurable multifunctions |c Charles Castaing ; Michel Valadier |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1977 | |
| 300 | |a VII, 278 S. | ||
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Record in the Search Index
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| adam_text | Contents
Chapter I. Convex Functions 1
§ 1 Convex lower semi continuous functions. Bipolar theorem .... 2
§ 2 Some properties of convex sets 7
§ 3 Inf compactness properties 12
§ 4 Infimum convolution 18
§ 5 Sub differentiability 24
§ 6 Some examples of mutually polar functions 29
Bibliography of Chapter I 35
Chapter II. Hausdorff Distance and Hausdorff Uniformity 37
§ 1 The space of closed subsets of a metric space 38
§ 2 The case of a uniform space. Hausdorff uniformity 44
§ 3 The space of closed convex subsets of a locally convex space 46
§ 4 Continuity of convex multi functions 51
Bibliography of Chapter II 56
Chapter III. Measurable Multi Functions 59
§ 0 Prerequisites 60
§ 1 Measurable multi functions, with values in compact subsets
of a metrizable separable space 62
§ 2 Selection theorem. Measurable multi functions with values
in complete subsets of a separable metric space 65
§ 3 Measurable compact convex multi functions 70
§ 4 Projection theorem. Von Neumann Aumann s selection theorem. 72
§ 5 Measurability in Suslin locally convex spaces 81
§ 6 Implicit function theorem. Stability properties of
measurable multi functions 85
Bibliography of Chapter III 89
VI
Chapter IV. Topological Property of the Profile of a Measurable
Multifunction with Compact Convex Values 91
§ 1 The main theorem and its corollaries 91
§ 2 Applications. Parametric version of Caratheodory1s theorem.
Parametric version of Choquet1s theorem 100
§ 3 Characterization of the profile of a convex set of
measurable selections 107
§ 4 Extension of Ljapunov1s theorem 112
Bibliography of Chapter IV 121
Chapter V. Compactness Theorems of Measurable Selections and
Integral Representation Theorem 125
§ 1 Compactness theorems in the spaces L_, (fi, ,y) and L_(n,(X,y). 125
§ 2 Inf compactness theorems 131
§ 3 Extreme points of certain convex sets of measurable
functions defined by unilateral integral constraints 140
§ 4 Compactness theorem in generalized Kothe functions spaces
and its applications 142
§ 5 Integral representation theorem of multifunctions from
a Kothe space to a locally convex Suslin space 151
§ 6 Characterization of a class of absolutely p summing
operators 156
§ 7 Closure theorem of the set of measurable selections of a
measurable multifunction 159
Bibliography of Chapter V 160
Chapter VI. Primitive of Multifunctions and Multivalued
Differential Equations 163
§ 1 Primitive of multifunction 163
§ 2 Derivation of multifunction of bounded variation 167
§ 3 Closure theorem involving the compactness property of
trajectories of multivalued differential equations 170
§ 4 Existence theorem of multivalued differential equations .... 174
§ 5 Selection theorem for a separately measurable and separately
absolutely continuous multifunction 187
Bibliography of Chapter VI 193
VII
Chapter VII. Convex Integrand on Locally Convex Spaces.
Applications 195
§ 1 Preliminary results of measurability 195
§ 2 Duality theorem of convex integral functionals for
locally convex Suslin spaces 199
§ 3 Duality theorem of convex integral functionals for
non separable reflexive Banach space 203
§ 4 Applications of the duality theorem of convex integral
functionals 215
Bibliography of Chapter VII 227
Chapter VIII. A Natural Supplement of L in the Dual of L *.
Applications 231
§ 1 Singular linear functionals on L°°. Statement of the
main theorem 232
§ 2 Representation of L m Stonian spaces 241
§ 3 First proof of the main theorem when E = M and y bounded .. 245
§ 4 Second proof of the main theorem when E = TR and y bounded . 2 46
§ 5 Proof of the main theorem when y is bounded 249
§ 6 Proof of the main theorem 252
§ 7 Polar of a convex function on L 253
§ 8 Conditional expectation of a random vector 255
§ 9 Conditional expectations of integrands and random sets 258
Bibliography of Chapter VIII 273
Subject Index 277
|
| any_adam_object | 1 |
| author | Castaing, Charles 1932- Valadier, Michel 1940- |
| author_GND | (DE-588)1030053537 (DE-588)1030055432 |
| author_facet | Castaing, Charles 1932- Valadier, Michel 1940- |
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| discipline | Mathematik |
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| id | DE-604.BV001974879 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:38:12Z |
| institution | BVB |
| isbn | 3540081445 0387081445 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001288107 |
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| physical | VII, 278 S. |
| publishDate | 1977 |
| publishDateSearch | 1977 |
| publishDateSort | 1977 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Castaing, Charles 1932- Verfasser (DE-588)1030053537 aut Convex analysis and measurable multifunctions Charles Castaing ; Michel Valadier Berlin [u.a.] Springer 1977 VII, 278 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 580 Analyse fonctionnelle Convexe functies gtt Fonctions convexes Convex functions Functional analysis Multifunktion (DE-588)4434824-1 gnd rswk-swf Mehrwertige Funktion (DE-588)4409125-4 gnd rswk-swf Konvexe Analysis (DE-588)4138566-4 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 s DE-604 Mehrwertige Funktion (DE-588)4409125-4 s Konvexe Analysis (DE-588)4138566-4 s Multifunktion (DE-588)4434824-1 s Valadier, Michel 1940- Verfasser (DE-588)1030055432 aut Lecture notes in mathematics 580 (DE-604)BV000676446 580 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001288107&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Castaing, Charles 1932- Valadier, Michel 1940- Convex analysis and measurable multifunctions Lecture notes in mathematics Analyse fonctionnelle Convexe functies gtt Fonctions convexes Convex functions Functional analysis Multifunktion (DE-588)4434824-1 gnd Mehrwertige Funktion (DE-588)4409125-4 gnd Konvexe Analysis (DE-588)4138566-4 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4434824-1 (DE-588)4409125-4 (DE-588)4138566-4 (DE-588)4018916-8 |
| title | Convex analysis and measurable multifunctions |
| title_auth | Convex analysis and measurable multifunctions |
| title_exact_search | Convex analysis and measurable multifunctions |
| title_full | Convex analysis and measurable multifunctions Charles Castaing ; Michel Valadier |
| title_fullStr | Convex analysis and measurable multifunctions Charles Castaing ; Michel Valadier |
| title_full_unstemmed | Convex analysis and measurable multifunctions Charles Castaing ; Michel Valadier |
| title_short | Convex analysis and measurable multifunctions |
| title_sort | convex analysis and measurable multifunctions |
| topic | Analyse fonctionnelle Convexe functies gtt Fonctions convexes Convex functions Functional analysis Multifunktion (DE-588)4434824-1 gnd Mehrwertige Funktion (DE-588)4409125-4 gnd Konvexe Analysis (DE-588)4138566-4 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Analyse fonctionnelle Convexe functies Fonctions convexes Convex functions Functional analysis Multifunktion Mehrwertige Funktion Konvexe Analysis Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001288107&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT castaingcharles convexanalysisandmeasurablemultifunctions AT valadiermichel convexanalysisandmeasurablemultifunctions |