Young measures and compactness in measure spaces
- Florescu, Liviu C.
- Berlin ; Boston : De Gruyter, c2012.
- Physical description
- xii, 339 p. : ill. ; 25 cm.
QA312 .F56 2012
- Unknown QA312 .F56 2012
- Godet-Thobie, Christiane.
- Includes bibliographical references (p. -335) and index.
- Preface: 1 Weak Compactness in Measure Spaces-- 1.1 Measure spaces-- 1.2 Radon-Nikodym theorem. The dual of-- 1 1.3 Convergences in L1 and ca(A) 1.4 Weak compactness in ca(A) and L1-- 1.5 The bidual of L1-- 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-- 2.6 Wiener measure-- 3 Young Measures-- 3.1 Preliminaries-- 3.2 Definitions. Examples-- 3.3 The stable topology-- 3.4 The subspace-- 3.5 Compactness-- 3.6 Biting lemma-- 3.7 Product of Young measures-- 3.8 Jordan finite tight sets-- 3.9 Strong compactness in Lp-- References-- Index.
- (source: Nielsen Book Data)
- Publisher's Summary
- 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 introduce the topic to postgraduate students and may also serve as a reference for more experienced researchers.
(source: Nielsen Book Data)
- Publication date
- Liviu C. Florescu, Christiane Godet-Thobie.