Saadoune, Mohammed; Valadier, Michel Extraction of a “good” subsequence from a bounded sequence of integrable functions. (English) Zbl 0833.46018 J. Convex Anal. 2, No. 1-2, 345-357 (1995). Summary: For a uniformly integrable sequence, the Young measures allow to precise the Dunford-Pettis theorem: there exists a subsequence and two complementary subsets above which one has strong convergence and “pure” weak \(L^1\)-convergence. For a bounded sequence in \(L^1\), the “biting lemma” permits the extraction of a subsequence presenting, besides the foregoing behaviors, concentration of mass. This structural result allows us to prove very quickly some known results. Cited in 12 Documents MSC: 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence Keywords:biting lemma; uniformly integrable sequence; Young measures; Dunford- Pettis theorem; strong convergence; weak \(L^ 1\)-convergence PDFBibTeX XMLCite \textit{M. Saadoune} and \textit{M. Valadier}, J. Convex Anal. 2, No. 1--2, 345--357 (1995; Zbl 0833.46018) Full Text: EuDML EMIS