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100   $a20120224d2012      uy             0
101 0 $aeng
135   $aurnn#---|u||u
181   $ctxt
182   $cc
183   $acr
200 10$aYoung measures and compactness in measure spaces$b[electronic resource] /$fLiviu C. Florescu, Christiane Godet-Thobie
210   $aBerlin ;$aBoston $cDe Gruyter$dc2012
215   $a1 online resource (352 p.)
300   $aDescription based upon print version of record.
311 0 $a3-11-027640-2 
320   $aIncludes bibliographical references and index.
327   $tFront matter --$tPreface --$tContents --$tChapter 1. Weak Compactness in Measure Spaces --$tChapter 2. Bounded Measures on Topological Spaces --$tChapter 3. Young Measures --$tBibliography --$tIndex --$tAbout the Authors
330   $aIn 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.
606   $aSpaces of measures
606   $aMeasure theory
606   $aMathematical optimization
610   $aBounded Measure.
610   $aFunctional Analysis.
610   $aMeasure Space.
610   $aTopological Space.
610   $aWeak Compactness.
610   $aYoung Measure.
615  0$aSpaces of measures.
615  0$aMeasure theory.
615  0$aMathematical optimization.
676   $a515/.42
686   $aSK 430$2rvk
700   $aFlorescu$b Liviu C$01195589
701   $aGodet-Thobie$b Christiane$01496133
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910790492103321
996   $aYoung measures and compactness in measure spaces$93720639
997   $aUNINA