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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Mean convergence and compact subsets of $ L\sb{1}$


Author: Benjamin Halpern
Journal: Proc. Amer. Math. Soc. 28 (1971), 122-126
MSC: Primary 28.20
MathSciNet review: 0276432
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Abstract: It is shown that in the usual criterion for $ w$ compactness of a set $ K$ in $ {L_1}(\mu )$ the explicit assumption that $ K$ is bounded follows from the other assumptions which are usually made if $ \mu $ is nonatomic.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0276432-3
PII: S 0002-9939(1971)0276432-3
Keywords: Mean convergenc, $ {L_1}$, equicontinuity, absolute continuity
Article copyright: © Copyright 1971 American Mathematical Society



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