Young measures on topological spaces: with applications in control theory and probability theory
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
2004
|
| Schriftenreihe: | Mathematics and its applications
571 |
| Schlagwörter: | |
| Links: | http://www.loc.gov/catdir/enhancements/fy0823/2004050401-d.html http://www.loc.gov/catdir/enhancements/fy0823/2004050401-t.html http://www.zentralblatt-math.org/zmath/en/search/?an=1067.28001 http://www.gbv.de/dms/goettingen/387704825.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025675067&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Includes indexes |
| Umfang: | XI, 320 S. |
| ISBN: | 1402019637 1402019645 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1819301828498554880 |
|---|---|
| adam_text | Titel: Young measures on topological spaces
Autor: Castaing, Charles
Jahr: 2004
Contents
Contents vii
Preface ix
1 Generalities, preliminary results 1
1.1 General topology............................ 1
1.2 Random elements, random sets, integrands ............. 5
1.3 Narrow and weak convergence of measures on a topological space . 12
1.4 Measurable cardinals and separable Borei measures......... 17
2 Young measures, the four stable topologies: S, M, N, W 19
2.1 Definitions, Portmanteau Theorem.................. 19
2.2 Special subspaces of Young measures, denseness of the space X of
random variables............................ 38
2.3 Properties of (y1,^,) related to the topology of T......... 42
2.4 Integrable Young measures and L| spaces.............. 44
3 Convergence in probability of Young measures (with some appli-
cations to stable convergence) 53
3.1 Stable convergence versus convergence in probability........ 53
3.2 Parametrized Dudley distances.................... 61
3.3 Fiber Product Lemma and applications............... 69
3.4 Parametrized Lévy-Wasserstein distances and L¿ spaces...... 74
4 Compactness 83
4.1 Preliminary remarks and definitions................. 83
4.2 Necessary and sufficient condition when T is separably submetriz-
able: Tops0e Criterion......................... 85
4.3 Flexible tightness and strict tightness: Prohorov Criterion..... 90
4.4 Submetrizable fcw-spaces, Change of Topology Lemma....... 100
4.5 Sequential properties: sequential Prohorov property, Komlós con-
vergence, Mazur-compactness..................... 104
viii CONTENTS
4.6 Tables.................................. 112
5 Strong tightness 115
5.1 Equivalent definitions ......................... 115
5.2 Strong tightness of a.e. convergent sequences............ 120
6 Young measures on Banach spaces. Applications 123
6.1 Preliminaries, Biting Lemma and some basic results........ 123
6.2 Weak convergence in L|(ìì,»S,P) using Young measures...... 141
6.3 Weak compactness and convergences in Pettis integration..... 147
6.4 Narrow compactness of Young measures via the Dudley embedding
theorem................................. 155
6.5 Support theorem for Young measures................. 166
6.6 Visintin-type theorem in P¿(íi, S, P)................. 180
6.7 Visintin-type theorem in L¿. [E] (0,5, P)............... 190
7 Applications in Control Theory 197
7.1 Measurable selection results...................... 197
7.2 Relaxed trajectories of an evolution equation governed by a maximal
monotone operator........................... 200
7.3 Relaxed trajectories of a differential inclusion in a Banach space . 205
7.4 Integral representation theorem via Young measures........ 209
7.5 Relaxed trajectories of a differential inclusion governed by a non-
convex sweeping process........................ 212
8 Semicontinuity of integral functionals using Young measures 219
8.1 Weak-strong lower semicontinuity of integral functionals...... 219
8.2 Reshetnyak-type theorems for Banach-valued measure....... 240
8.3 Some new applications of the Fiber Product Lemma for Young mea-
sures ................................... 250
8.3.A The value function of a control problem governed by a first
order ordinary differential equation.............. 251
8.3.B Dynamic programming..................... 259
9 Stable convergence in limit theorems of probability theory 271
9.1 Weak limit theorems in locally convex spaces............ 271
9.2 More on stable convergence...................... 275
9.3 Rényi-mixing Central Limit Theorem for a-mixing sequences ... 281
9.4 Stable Central Limit Theorem for a random number of random
vectors.................................. 284
References 295
Subject Index 315
Index of Notations 319
|
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| id | DE-604.BV040694408 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T16:23:32Z |
| institution | BVB |
| isbn | 1402019637 1402019645 |
| language | English |
| lccn | 2004050401 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025675067 |
| oclc_num | 249627186 |
| open_access_boolean | 1 |
| owner | DE-824 |
| owner_facet | DE-824 |
| physical | XI, 320 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spellingShingle | Castaing, Charles 1932- Raynaud de Fitte, Paul 1954- Valadier, Michel 1940- Young measures on topological spaces with applications in control theory and probability theory Mathematics and its applications Young-Maß (DE-588)4513824-2 gnd Topologischer Raum (DE-588)4137586-5 gnd |
| subject_GND | (DE-588)4513824-2 (DE-588)4137586-5 |
| title | Young measures on topological spaces with applications in control theory and probability theory |
| title_auth | Young measures on topological spaces with applications in control theory and probability theory |
| title_exact_search | Young measures on topological spaces with applications in control theory and probability theory |
| title_full | Young measures on topological spaces with applications in control theory and probability theory by Charles Castaing, Paul Raynaud de Fitte and Michel Valadier |
| title_fullStr | Young measures on topological spaces with applications in control theory and probability theory by Charles Castaing, Paul Raynaud de Fitte and Michel Valadier |
| title_full_unstemmed | Young measures on topological spaces with applications in control theory and probability theory by Charles Castaing, Paul Raynaud de Fitte and Michel Valadier |
| title_short | Young measures on topological spaces |
| title_sort | young measures on topological spaces with applications in control theory and probability theory |
| title_sub | with applications in control theory and probability theory |
| topic | Young-Maß (DE-588)4513824-2 gnd Topologischer Raum (DE-588)4137586-5 gnd |
| topic_facet | Young-Maß Topologischer Raum |
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