Extraction of a 'Good' Subsequence from a Bounded Sequence of Integrable Functions

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 L¹ -convergence. For a bounded sequence in L¹ , 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.