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Proceedings of the American Mathematical Society

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Remarks on Chacon's biting lemma


Authors: J. M. Ball and F. Murat
Journal: Proc. Amer. Math. Soc. 107 (1989), 655-663
MSC: Primary 46G10; Secondary 46E40, 49A50
MathSciNet review: 984807
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Abstract: Chacon's Biting Lemma states roughly that any bounded sequence in $ {L^1}$ possesses a subsequence converging weakly in $ {L^1}$ outside a decreasing family $ {E_k}$ of measurable sets with vanishingly small measure. A simple new proof of this result is presented that makes explicit which sets $ {E_k}$ need to be removed. The proof extends immediately to the case when the functions take values in a reflexive Banach space. The limit function is identified via the Young measure and approximations. The description of concentration provided by the lemma is discussed via a simple example.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0984807-3
Keywords: Chacon Biting Lemma, weak convergence, concentration, Young measure, truncation
Article copyright: © Copyright 1989 American Mathematical Society