Young Measures and Compactness in Measure Spaces.:
Many problems in science can be formulated in the language of optimization theory, in which case an optimal solution or the best response to a particular situation is required. In situations of interest, such classical optimal solutions are lacking, or at least, the existence of such solutions is fa...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin :
De Gruyter,
2012.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Many problems in science can be formulated in the language of optimization theory, in which case an optimal solution or the best response to a particular situation is required. In situations of interest, such classical optimal solutions are lacking, or at least, the existence of such solutions is far from easy to prove. So, non-convex optimization problems may not possess a classical solution because approximate solutions typically show rapid oscillations. This phenomenon requires the extension of such problems' solution often constructed by means of Young measures. This book is written to int. |
| Beschreibung: | 1 online resource (352 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9783110280517 3110280515 |
Internformat
MARC
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| 245 | 1 | 0 | |a Young Measures and Compactness in Measure Spaces. |
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| 300 | |a 1 online resource (352 pages) | ||
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| 588 | 0 | |a Print version record. | |
| 520 | |a Many problems in science can be formulated in the language of optimization theory, in which case an optimal solution or the best response to a particular situation is required. In situations of interest, such classical optimal solutions are lacking, or at least, the existence of such solutions is far from easy to prove. So, non-convex optimization problems may not possess a classical solution because approximate solutions typically show rapid oscillations. This phenomenon requires the extension of such problems' solution often constructed by means of Young measures. This book is written to int. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | 0 | |t Frontmatter -- |t Preface -- |t Contents -- |t Chapter 1. Weak Compactness in Measure Spaces -- |t Chapter 2. Bounded Measures on Topological Spaces -- |t Chapter 3. Young Measures -- |t Bibliography -- |t Index -- |t About the Authors. |
| 546 | |a English. | ||
| 650 | 0 | |a Spaces of measures. |0 http://id.loc.gov/authorities/subjects/sh85126022 | |
| 650 | 0 | |a Measure theory. |0 http://id.loc.gov/authorities/subjects/sh85082702 | |
| 650 | 0 | |a Mathematical optimization. |0 http://id.loc.gov/authorities/subjects/sh85082127 | |
| 650 | 4 | |a Bounded Measures. | |
| 650 | 4 | |a Measure Spaces. | |
| 650 | 4 | |a Topological Spaces. | |
| 650 | 4 | |a Weak Compactness. | |
| 650 | 4 | |a Young Measures. | |
| 650 | 6 | |a Espaces de mesures. | |
| 650 | 6 | |a Théorie de la mesure. | |
| 650 | 6 | |a Optimisation mathématique. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
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| 650 | 7 | |a Measure theory |2 fast | |
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| 700 | 1 | |a Godet-Thobie, Christiane. | |
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| 776 | 0 | 8 | |i Print version: |a Florescu, Liviu C. |t Young Measures and Compactness in Measure Spaces. |d Berlin : De Gruyter, ©2012 |z 9783110276404 |
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| 880 | 0 | |6 505-00/(S |a Machine generated contents note: 1. Weak Compactness in Measure Spaces -- 1.1. Measure Spaces -- 1.2. Radon-Nikodym Theorem. The Dual of L1 -- 1.3. Convergences in L1(λ) and ca(A) -- 1.4. Weak Compactness in ca(A) and L1(λ) -- 1.5. The Bidual of L1(λ) -- 1.6. Extensions of Dunford-Pettis' Theorem -- 2. Bounded Measures on Topological Spaces -- 2.1. Regular Measures -- 2.2. Polish Spaces. Suslin Spaces -- 2.3. Narrow Topology -- 2.4.Compactness Results -- 2.5. Metrics on the Space (Rca+(BT), J) -- 2.5.1. Dudley's Metric -- 2.5.2. Levy-Prohorov's Metric -- 2.6. Wiener Measure -- 3. Young Measures -- 3.1. Preliminaries -- 3.1.1. Disintegration -- 3.1.2. Integrands -- 3.2. Definitions and Examples -- 3.2.1. Young Measure Associated to a Probability -- 3.2.2. Young Measure Associated to a Measurable Mapping -- 3.3. The Stable Topology -- 3.4. The Subspace M(S) [⊂] y(S) -- 3.5.Compactness -- 3.6. Biting Lemma -- 3.7. Product of Young Measures -- 3.7.1. Fiber Product. | |
| 880 | 0 | |6 505-00/(S |a Contents note continued: 3.7.2. Tensor Product -- 3.8. Jordan Finite Tight Sets -- 3.9. Strong Compactness in Lp(μ, E) -- 3.9.1. Visintin-Balder's Theorem -- 3.9.2. Rossi-Savare's Theorem -- 3.10. Gradient Young Measures -- 3.10.1. Young Measures Generated by Sequences -- 3.10.2. Quasiconvex Functions -- 3.10.3. Lower Semicontinuity -- 3.11. Relaxed Solutions in Variational Calculus. | |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn796384258 |
|---|---|
| _version_ | 1816881799183204352 |
| adam_text | |
| any_adam_object | |
| author | Florescu, Liviu C. |
| author2 | Godet-Thobie, Christiane |
| author2_role | |
| author2_variant | c g t cgt |
| author_facet | Florescu, Liviu C. Godet-Thobie, Christiane |
| author_role | |
| author_sort | Florescu, Liviu C. |
| author_variant | l c f lc lcf |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA312 |
| callnumber-raw | QA312 .F56 2012 |
| callnumber-search | QA312 .F56 2012 |
| callnumber-sort | QA 3312 F56 42012 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 430 |
| collection | ZDB-4-EBA |
| contents | Frontmatter -- Preface -- Contents -- Chapter 1. Weak Compactness in Measure Spaces -- Chapter 2. Bounded Measures on Topological Spaces -- Chapter 3. Young Measures -- Bibliography -- Index -- About the Authors. |
| ctrlnum | (OCoLC)796384258 |
| dewey-full | 515.42 515/.42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.42 515/.42 |
| dewey-search | 515.42 515/.42 |
| dewey-sort | 3515.42 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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Weak Compactness in Measure Spaces -- 1.1. Measure Spaces -- 1.2. Radon-Nikodym Theorem. The Dual of L1 -- 1.3. Convergences in L1(λ) and ca(A) -- 1.4. Weak Compactness in ca(A) and L1(λ) -- 1.5. The Bidual of L1(λ) -- 1.6. Extensions of Dunford-Pettis' Theorem -- 2. Bounded Measures on Topological Spaces -- 2.1. Regular Measures -- 2.2. Polish Spaces. Suslin Spaces -- 2.3. Narrow Topology -- 2.4.Compactness Results -- 2.5. Metrics on the Space (Rca+(BT), J) -- 2.5.1. Dudley's Metric -- 2.5.2. Levy-Prohorov's Metric -- 2.6. Wiener Measure -- 3. Young Measures -- 3.1. Preliminaries -- 3.1.1. Disintegration -- 3.1.2. Integrands -- 3.2. Definitions and Examples -- 3.2.1. Young Measure Associated to a Probability -- 3.2.2. Young Measure Associated to a Measurable Mapping -- 3.3. The Stable Topology -- 3.4. The Subspace M(S) [⊂] y(S) -- 3.5.Compactness -- 3.6. Biting Lemma -- 3.7. Product of Young Measures -- 3.7.1. Fiber Product.</subfield></datafield><datafield tag="880" ind1="0" ind2=" "><subfield code="6">505-00/(S</subfield><subfield code="a">Contents note continued: 3.7.2. Tensor Product -- 3.8. Jordan Finite Tight Sets -- 3.9. Strong Compactness in Lp(μ, E) -- 3.9.1. Visintin-Balder's Theorem -- 3.9.2. Rossi-Savare's Theorem -- 3.10. Gradient Young Measures -- 3.10.1. Young Measures Generated by Sequences -- 3.10.2. Quasiconvex Functions -- 3.10.3. Lower Semicontinuity -- 3.11. 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| id | ZDB-4-EBA-ocn796384258 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:18:27Z |
| institution | BVB |
| isbn | 9783110280517 3110280515 |
| language | English |
| oclc_num | 796384258 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (352 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | De Gruyter, |
| record_format | marc |
| spelling | Florescu, Liviu C. Young Measures and Compactness in Measure Spaces. Berlin : De Gruyter, 2012. 1 online resource (352 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Print version record. Many problems in science can be formulated in the language of optimization theory, in which case an optimal solution or the best response to a particular situation is required. In situations of interest, such classical optimal solutions are lacking, or at least, the existence of such solutions is far from easy to prove. So, non-convex optimization problems may not possess a classical solution because approximate solutions typically show rapid oscillations. This phenomenon requires the extension of such problems' solution often constructed by means of Young measures. This book is written to int. Includes bibliographical references and index. Frontmatter -- Preface -- Contents -- Chapter 1. Weak Compactness in Measure Spaces -- Chapter 2. Bounded Measures on Topological Spaces -- Chapter 3. Young Measures -- Bibliography -- Index -- About the Authors. English. Spaces of measures. http://id.loc.gov/authorities/subjects/sh85126022 Measure theory. http://id.loc.gov/authorities/subjects/sh85082702 Mathematical optimization. http://id.loc.gov/authorities/subjects/sh85082127 Bounded Measures. Measure Spaces. Topological Spaces. Weak Compactness. Young Measures. Espaces de mesures. Théorie de la mesure. Optimisation mathématique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Mathematical optimization fast Measure theory fast Spaces of measures fast Maßraum gnd http://d-nb.info/gnd/4169057-6 Kompaktheit gnd http://d-nb.info/gnd/4456100-3 Young-Maß gnd http://d-nb.info/gnd/4513824-2 Godet-Thobie, Christiane. has work: Young measures and compactness in measure spaces (Text) https://id.oclc.org/worldcat/entity/E39PCYDv7FWBP98vVT4XgWrXMK https://id.oclc.org/worldcat/ontology/hasWork Print version: Florescu, Liviu C. Young Measures and Compactness in Measure Spaces. Berlin : De Gruyter, ©2012 9783110276404 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=471034 Volltext 505-00/(S Machine generated contents note: 1. Weak Compactness in Measure Spaces -- 1.1. Measure Spaces -- 1.2. Radon-Nikodym Theorem. The Dual of L1 -- 1.3. Convergences in L1(λ) and ca(A) -- 1.4. Weak Compactness in ca(A) and L1(λ) -- 1.5. The Bidual of L1(λ) -- 1.6. Extensions of Dunford-Pettis' Theorem -- 2. Bounded Measures on Topological Spaces -- 2.1. Regular Measures -- 2.2. Polish Spaces. Suslin Spaces -- 2.3. Narrow Topology -- 2.4.Compactness Results -- 2.5. Metrics on the Space (Rca+(BT), J) -- 2.5.1. Dudley's Metric -- 2.5.2. Levy-Prohorov's Metric -- 2.6. Wiener Measure -- 3. Young Measures -- 3.1. Preliminaries -- 3.1.1. Disintegration -- 3.1.2. Integrands -- 3.2. Definitions and Examples -- 3.2.1. Young Measure Associated to a Probability -- 3.2.2. Young Measure Associated to a Measurable Mapping -- 3.3. The Stable Topology -- 3.4. The Subspace M(S) [⊂] y(S) -- 3.5.Compactness -- 3.6. Biting Lemma -- 3.7. Product of Young Measures -- 3.7.1. Fiber Product. 505-00/(S Contents note continued: 3.7.2. Tensor Product -- 3.8. Jordan Finite Tight Sets -- 3.9. Strong Compactness in Lp(μ, E) -- 3.9.1. Visintin-Balder's Theorem -- 3.9.2. Rossi-Savare's Theorem -- 3.10. Gradient Young Measures -- 3.10.1. Young Measures Generated by Sequences -- 3.10.2. Quasiconvex Functions -- 3.10.3. Lower Semicontinuity -- 3.11. Relaxed Solutions in Variational Calculus. |
| spellingShingle | Florescu, Liviu C. Young Measures and Compactness in Measure Spaces. Frontmatter -- Preface -- Contents -- Chapter 1. Weak Compactness in Measure Spaces -- Chapter 2. Bounded Measures on Topological Spaces -- Chapter 3. Young Measures -- Bibliography -- Index -- About the Authors. Spaces of measures. http://id.loc.gov/authorities/subjects/sh85126022 Measure theory. http://id.loc.gov/authorities/subjects/sh85082702 Mathematical optimization. http://id.loc.gov/authorities/subjects/sh85082127 Bounded Measures. Measure Spaces. Topological Spaces. Weak Compactness. Young Measures. Espaces de mesures. Théorie de la mesure. Optimisation mathématique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Mathematical optimization fast Measure theory fast Spaces of measures fast Maßraum gnd http://d-nb.info/gnd/4169057-6 Kompaktheit gnd http://d-nb.info/gnd/4456100-3 Young-Maß gnd http://d-nb.info/gnd/4513824-2 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85126022 http://id.loc.gov/authorities/subjects/sh85082702 http://id.loc.gov/authorities/subjects/sh85082127 http://d-nb.info/gnd/4169057-6 http://d-nb.info/gnd/4456100-3 http://d-nb.info/gnd/4513824-2 |
| title | Young Measures and Compactness in Measure Spaces. |
| title_alt | Frontmatter -- Preface -- Contents -- Chapter 1. Weak Compactness in Measure Spaces -- Chapter 2. Bounded Measures on Topological Spaces -- Chapter 3. Young Measures -- Bibliography -- Index -- About the Authors. |
| title_auth | Young Measures and Compactness in Measure Spaces. |
| title_exact_search | Young Measures and Compactness in Measure Spaces. |
| title_full | Young Measures and Compactness in Measure Spaces. |
| title_fullStr | Young Measures and Compactness in Measure Spaces. |
| title_full_unstemmed | Young Measures and Compactness in Measure Spaces. |
| title_short | Young Measures and Compactness in Measure Spaces. |
| title_sort | young measures and compactness in measure spaces |
| topic | Spaces of measures. http://id.loc.gov/authorities/subjects/sh85126022 Measure theory. http://id.loc.gov/authorities/subjects/sh85082702 Mathematical optimization. http://id.loc.gov/authorities/subjects/sh85082127 Bounded Measures. Measure Spaces. Topological Spaces. Weak Compactness. Young Measures. Espaces de mesures. Théorie de la mesure. Optimisation mathématique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Mathematical optimization fast Measure theory fast Spaces of measures fast Maßraum gnd http://d-nb.info/gnd/4169057-6 Kompaktheit gnd http://d-nb.info/gnd/4456100-3 Young-Maß gnd http://d-nb.info/gnd/4513824-2 |
| topic_facet | Spaces of measures. Measure theory. Mathematical optimization. Bounded Measures. Measure Spaces. Topological Spaces. Weak Compactness. Young Measures. Espaces de mesures. Théorie de la mesure. Optimisation mathématique. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Mathematical optimization Measure theory Spaces of measures Maßraum Kompaktheit Young-Maß |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=471034 |
| work_keys_str_mv | AT floresculiviuc youngmeasuresandcompactnessinmeasurespaces AT godetthobiechristiane youngmeasuresandcompactnessinmeasurespaces |