Weak sequential convergence in \(L_ 1(\mu,X)\) and an approximate version of Fatou's lemma

DOI10.1016/0022-247X(86)90108-3zbMath0602.46033OpenAlexW2103767223WikidataQ124880645 ScholiaQ124880645MaRDI QIDQ1081806

M. Ali Khan, Mukul K. Majumdar

Publication date: 1986

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(86)90108-3

zbMATH Keywords

Hahn-Banach theoremweak limitBochner integrable functionsmeasurability of the graph of the limit point correspondence

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) Vector-valued measures and integration (46G10)

Related Items

An exact Fatou lemma for Gelfand integrals: a characterization of the Fatou property ⋮ A general Fatou lemma ⋮ A counterexample and an exact version of Fatou's lemma in infinite dimensional spaces ⋮ Fatou's lemma in infinite dimensions ⋮ Weak sequential convergence in \(L_ p(\mu,X)\) ⋮ Integration of Correspondences on Loeb Spaces ⋮ On Cournot–Nash equilibria in generalized qualitative games with a continuum of players ⋮ Fatou's lemmas for the set of integrable selections ⋮ Pure-strategy Nash equilibria in nonatomic games with infinite-dimensional action spaces ⋮ On Fatou's lemma and parametric integrals for set-valued functions ⋮ Weak sequential convergence in \(L^1(\mu,X)\) and an exact version of Fatou's lemma ⋮ Convergence theorems for Pettis integrable functions and regular methods of summability ⋮ Measurability and integrability of the weak upper limit of a sequence of multifunctions ⋮ On the upper and lower semicontinuity of the Aumann integral ⋮ 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 ⋮ Applications of the method of compactness and decomposition: minimization, convergence of martingales, multivalued Fatou lemma ⋮ On a paper by Khan and Majumdar

Cites Work

• A note on Fatou's lemma in several dimensions
• Convex analysis and measurable multifunctions
• Remarks on Weak Compactness in L₁(μ,X)
• Measurability and Pettis integration in Hilbert spaces.
• Weak Sequential Convergence in L ∞ E and Dunford-Pettis Property of L 1 E
• On fixed point theorems for random set-valued maps
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item