Compacité faible dans l'espace \(L^ 1_ E\) et dans l'espace des multifonctions intégralement bornées, et minimisation. (Weak compactness in the space \(L^ 1_ E\) and in the space of integrally bounded multifunctions, and minimization)

DOI10.1007/BF01776856zbMath0606.28006MaRDI QIDQ1084528

Charles Castaing, Paulette Clauzure

Publication date: 1985

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

zbMATH Keywords

compactness resultsapplications to minimization problemsBochner integrable functions in Banach spacesintegrally bounded multifunctions

Mathematics Subject Classification ID

Set-valued set functions and measures; integration of set-valued functions; measurable selections (28B20) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Vector-valued measures and integration (46G10)

Related Items (6)

Weakly compact subsets of \(L_ 1(\mu ,X)\) and \(bvca(\Sigma , X)\) ⋮ New results in the theory of multivalued mappings. I: Topological characteristics and solvability of operator relations ⋮ A Komlós-type theorem for the set-valued Henstock-Kurzweil-Pettis integral and applications ⋮ Weak Compactness Criteria for Set Valued Integrals and Radon Nikodym Theorem for Vector Valued Multimeasures ⋮ Applications of the method of compactness and decomposition: minimization, convergence of martingales, multivalued Fatou lemma ⋮ M-convergence, et régularité des martingales multivoques: Epi- martingales. (M-convergence and regularity of multivalued martingales: Epi-martingales)

Cites Work

• Convex analysis and measurable multifunctions
• Weak compactness in spaces of Bochner integrable functions and applications
• Best ?- and N ?-approximants in Orlicz spaces of vector valued functions
• Best approximants in L 1 space
• Weak Convergence of Set-Valued Functions and Control
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