This article is cited in 1 paper

Remarks on mean convergence

P. L. Ul'yanov

M. V. Lomonosov Moscow State University

Abstract: In this article a necessary and sufficient condition is established for the validity of the Cauchy criterion in the class of sequences of functions $\{f_n\}$ of the set $\varphi(L)$ which are convergent with respect to the $\varphi$-distance.

UDC: 517.5

Received: 11.11.1976

 English version: Mathematical Notes, 1977, 21:6, 455–461

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