This article is cited in 3 papers

Rearrangements of series in $L_p$

E. M. Nikishin

M. V. Lomonosov Moscow State University

Abstract: In this note we show that the condition
$$\sqrt{\sum_{n=1}^\infty f_n^2(x)}\in L_p$$
is sufficient for the set of sums of the rearranged series $\Sigma_\sigma f_n$ to be a closed linear set in $L_p$.

UDC: 517.5

Received: 21.02.1973

 English version: Mathematical Notes, 1973, 14:1, 570–574

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