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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.

References [Enhancements On Off] (What's this?)

  • [1] Nelson Dunford and Jacob T. Schwartz, Linear operators. I: General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958. MR 22 #8302. MR 0117523 (22:8302)
  • [2] Paul R. Halmos, Measure theory, Van Nostrand, Princeton, N. J., 1950. MR 11, 504. MR 0033869 (11:504d)

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Keywords: Mean convergenc, $ {L_1}$, equicontinuity, absolute continuity
Article copyright: © Copyright 1971 American Mathematical Society

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