Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Mohammed Saadoune

Département de Mathématiques, Université Ibnou Zohr, Lot. Addakhala B.P. 28/S, Agadir, Marocco.

Michel Valadier

Département de Mathématiques — Case 051, Université Montpellier II, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France.

Keywords

  • Bounded sequences in L¹
  • biting lemma
  • Young measures
  • uniform integrability

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Suggested citation

M. Saadoune, M. Valadier. “Extraction of a 'Good' Subsequence from a Bounded Sequence of Integrable Functions.” Journal of Convex Analysis 2 (1995), No. 1&2, 345–357. https://doi.org/10.68381/jca02022

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Published by Heldermann Verlag, 1995. Rights now held by Banach Press LLC.