Young Measures on Topological Spaces: with Applications in Control Theory and Probability Theory by Charles CastaingYoung Measures on Topological Spaces: with Applications in Control Theory and Probability Theory by Charles Castaing

Young Measures on Topological Spaces: with Applications in Control Theory and Probability Theory

byCharles Castaing, Paul Raynaud de Fitte, Michel Valadier

Paperback | December 4, 2010

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Young measures are now a widely used tool in the Calculus of Variations, in Control Theory, in Probability Theory and other fields. They are known under different names such as "relaxed controls", "fuzzy random variables" and many other names. This monograph provides a unified presentation of the theory, along with new results and applications in various fields. It can serve as a reference on the subject. Young measures are presented in a general setting which includes finite and for the first time infinite dimensional spaces: the fields of applications of Young measures (Control Theory, Calculus of Variations, Probability Theory...) are often concerned with problems in infinite dimensional settings. The theory of Young measures is now well understood in a finite dimensional setting, but open problems remain in the infinite dimensional case. We provide several new results in the general frame, which are new even in the finite dimensional setting, such as characterizations of convergence in measure of Young measures (Chapter 3) and compactness criteria (Chapter 4).These results are established under a different form (and with fewer details and developments) in recent papers by the same authors. We also provide new applications to Visintin and Reshetnyak type theorems (Chapters 6 and 8), existence of solutions to differential inclusions (Chapter 7), dynamical programming (Chapter 8) and the Central Limit Theorem in locally convex spaces (Chapter 9).

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Title:Young Measures on Topological Spaces: with Applications in Control Theory and Probability TheoryFormat:PaperbackDimensions:331 pages, 9.25 × 6.1 × 0 inPublished:December 4, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048165520

ISBN - 13:9789048165520

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Table of Contents

Preface.Generalities, Preliminary results.Young Measures, the four Stable Topologies: S, M, N, W.Convergence in Probability of Young Measures (with some applications to stable convergence).Compactness.Strong Tightness.Young Measures on Banach Spaces. Application.Applications in Control Theory.Semicontinuity of Integral Functionals using Young Measures.Stable Convergence in Limit Theorems of Probability Theory.

Editorial Reviews

From the reviews:"This book presents a wealth of results on Young measures on topological spaces in a very general framework. It is very likely that it will become the reference and starting point for any further developments in the field." (Georg K. Dolzmann, Mathematical Reviews, 2005k)