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 | References | Similar Articles | Additional Information

Abstract: Chacon's Biting Lemma states roughly that any bounded sequence in possesses a subsequence converging weakly in outside a decreasing family of measurable sets with vanishingly small measure. A simple new proof of this result is presented that makes explicit which sets 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

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