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Extraction of a “good” subsequence from a bounded sequence of integrable functions. (English) Zbl 0833.46018
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.

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
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