Mean convergence and compact subsets of
Abstract: It is shown that in the usual criterion for compactness of a set in the explicit assumption that is bounded follows from the other assumptions which are usually made if is nonatomic.
-  Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958. MR 0117523
-  Paul R. Halmos, Measure Theory, D. Van Nostrand Company, Inc., New York, N. Y., 1950. MR 0033869
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Keywords: Mean convergenc, , equicontinuity, absolute continuity
Article copyright: © Copyright 1971 American Mathematical Society