03873nam 2200733 a 450 991079049210332120230801223721.01-283-85791-X3-11-028051-53-11-028052-310.1515/9783110280517(CKB)2670000000211095(EBL)893352(OCoLC)796384258(SSID)ssj0000747503(PQKBManifestationID)12333058(PQKBTitleCode)TC0000747503(PQKBWorkID)10704082(PQKB)10252398(MiAaPQ)EBC893352(DE-B1597)175563(OCoLC)840444063(DE-B1597)9783110280517(Au-PeEL)EBL893352(CaPaEBR)ebr10582262(CaONFJC)MIL417041(EXLCZ)99267000000021109520120224d2012 uy 0engurnn#---|u||utxtccrYoung measures and compactness in measure spaces[electronic resource] /Liviu C. Florescu, Christiane Godet-ThobieBerlin ;Boston De Gruyterc20121 online resource (352 p.)Description based upon print version of record.3-11-027640-2 Includes bibliographical references and index.Front matter --Preface --Contents --Chapter 1. Weak Compactness in Measure Spaces --Chapter 2. Bounded Measures on Topological Spaces --Chapter 3. Young Measures --Bibliography --Index --About the AuthorsIn recent years, technological progress created a great need for complex mathematical models. Many practical problems can be formulated using optimization theory and they hope to obtain an optimal solution. In most cases, such optimal solution can not be found. So, non-convex optimization problems (arising, e.g., in variational calculus, optimal control, nonlinear evolutions equations) may not possess a classical minimizer because the minimizing sequences have typically rapid oscillations. This behavior requires a relaxation of notion of solution for such problems; often we can obtain such a relaxation by means of Young measures. This monograph is a self-contained book which gathers all theoretical aspects related to the defining of Young measures (measurability, disintegration, stable convergence, compactness), a book which is also a useful tool for those interested in theoretical foundations of the measure theory. It provides a complete set of classical and recent compactness results in measure and function spaces. The book is organized in three chapters: The first chapter covers background material on measure theory in abstract frame. In the second chapter the measure theory on topological spaces is presented. Compactness results from the first two chapters are used to study Young measures in the third chapter. All results are accompanied by full demonstrations and for many of these results different proofs are given. All statements are fully justified and proved.Spaces of measuresMeasure theoryMathematical optimizationBounded Measure.Functional Analysis.Measure Space.Topological Space.Weak Compactness.Young Measure.Spaces of measures.Measure theory.Mathematical optimization.515/.42SK 430rvkFlorescu Liviu C1195589Godet-Thobie Christiane1496133MiAaPQMiAaPQMiAaPQBOOK9910790492103321Young measures and compactness in measure spaces3720639UNINA