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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Remarks on Chacon’s biting lemma
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by J. M. Ball and F. Murat PDF
Proc. Amer. Math. Soc. 107 (1989), 655-663 Request permission

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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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 107 (1989), 655-663
  • MSC: Primary 46G10; Secondary 46E40, 49A50
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0984807-3
  • MathSciNet review: 984807