An averaging result for \(l^ 1-\)sequences and applications to weakly conditionally compact sets in \(L^ 1\).

DOI10.1007/BF02760458zbMath0464.60005MaRDI QIDQ1154172

Jean Bourgain

Publication date: 1979

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Radon probability spacevector valued function classes on Radon probability spaceweakly conditionally compact

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Vector-valued set functions, measures and integrals (28B05)

Related Items

Topological Equivalence in the Space of Integrable Vector-Valued Functions, On weak compactness in Lebesgue-Bochner spaces, Strongly Asplund generated and strongly conditionally weakly compactly generated Banach spaces, Strictly singular and strictly cosingular operators on spaces of continuous functions, On (V*) sets and Pelczynski's property (V*), Completely continuous operators and the strict topology, The weak Banach-Saks property on L^p(μ, E), On the Banach spaces with the property \((V^*)\) of Pelczynski, On the Dunford-Pettis Property, On the SWCG property in Lebesgue-Bochner spaces, On compactness in \(L_p(\mu,X)\) in the weak topology and in the topology \(\sigma(L_p(\mu,X),L_q(\mu,X'))\), Weakly \(p\)-Dunford Pettis sets in \(L_1(\mu,X)\), Some classes of continuous operators on spaces of bounded vector-valued continuous functions with the strict topology, A class of weakly compact sets in Lebesgue-Bochner spaces, On the Conditional Expectation and Convergence Properties of Random Sets, \(c_{0}\)-singular and \(\ell_{1}\)-singular operators between vector-valued Banach lattices, STRONGLY BOUNDED REPRESENTING MEASURES AND CONVERGENCE THEOREMS, Extensions of some classes of operators and applications, Contributions to the Theory of Set Valued Functions and Set Valued Measures, Weak precompactness, strong boundedness, and weak complete continuity, Weak compactness in 𝐿¹(𝜇,𝑋), Bases of random unconditional convergence in Banach spaces, On some subsets of $L_1(\mu,E)$, Another proof of a result of N. J. Kalton, E. Saab and P. Saab on the Dieudonné property in C(K, E), Relaxation methods for optimal control problems, Evolutions governed by m-accretive plus compact operators, $\varepsilon $-weakly precompact sets in Banach spaces, (Non-)Dunford-Pettis operators on noncommutative symmetric spaces

Cites Work

• A double-dual characterization of separable Banach spaces containing \(\ell^1\)
• Uniformly non-square Banach spaces
• Pointwise Compact Sets of Baire-Measurable Functions
• A Characterization of Banach Spaces Containing l ¹
• Point-Wise Compact Subsets of the First Baire Class
• A separable somewhat reflexive Banach space with nonseparable dual
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item