Truncation methods applied to problems of weak or strong convergence in \(L^ 1\)

DOI10.1007/BF00387764zbMath0778.46016MaRDI QIDQ1192278

Allal Amrani, Michel Valadier, Charles Castaing

Publication date: 27 September 1992

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

zbMATH Keywords

tightnessYoung measurecompactly uniformly integrablecompactness assumptionsE)\)weak or strong convergence of sequences in the space \(L^ 1(\Omega,\mu

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Spaces of vector- and operator-valued functions (46E40) Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence (28A20)

Related Items (14)

From weak to strong convergence in \(L_ 1\)-spaces via \(K\)-convergence ⋮ Young measures, weak and strong convergence and the Visintin-Balder theorem ⋮ Two-scale convergence of some integral functionals ⋮ An extension of the usual model in statistical decision theory with applications to stochastic optimization problems ⋮ Evolution Problems with Time-Dependent Subdifferential Operators ⋮ Property \((H)\) in Köthe-Bochner spaces ⋮ Characterisations of classes of multivalued processes using Riesz approximations ⋮ Convergences in a dual space with applications to Fatou lemma ⋮ Tightness conditions and integrability of the sequential weak upper limit of a sequence of multifunctions ⋮ CM-selectors for pairs of oppositely semicontinuous multifunctions and some applications to strongly nonlinear inclusions ⋮ On consistency of stationary points of stochastic optimization problems in a Banach space ⋮ A New Version of the Multivalued Fatou Lemma ⋮ On the theory of Banach space valued multifunctions. II: Set valued martingales and set valued measures ⋮ M-convergence, et régularité des martingales multivoques: Epi- martingales. (M-convergence and regularity of multivalued martingales: Epi-martingales)

Cites Work

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• Measurability and integrability of the weak upper limit of a sequence of multifunctions
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• A General Approach to Lower Semicontinuity and Lower Closure in Optimal Control Theory
• On weak convergence implying strong convergence in L₁-spaces
• Characterizations of Denting Points
• Strong convergence of selections implied by weak
• Fatou's Lemma in Infinite-Dimensional Spaces
• On Fatou's Lemma in several dimensions
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