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 Mat. Zametki, 1972, Volume 11, Issue 5, Pages 481–490 (Mi mz9814)

On a property of functional series

B. S. Kashin

M. V. Lomonosov Moscow State University

Abstract: The question of the convergence of functional series everywhere in the segment $[0, 1]$ is considered. Let $F=\{f\}$ be the set of such functions in $[0, 1]$ for each of which there is a transposition of the series $\sum_{k=1}^\infty f_k(x)$, which converges to it everywhere in $[0, 1]$. An example of a series is constructed such that the set $F$ consists just of an identical zero, but $\sum_{k=1}^\infty|f_k(x_0)|=\infty$ ($x_0\in[0,1]$) for any point of the segment $[0, 1]$.

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English version:
Mathematical Notes, 1972, 11:5, 294–299

Bibliographic databases:

UDC: 517.5

Citation: B. S. Kashin, “On a property of functional series”, Mat. Zametki, 11:5 (1972), 481–490; Math. Notes, 11:5 (1972), 294–299

Citation in format AMSBIB
\Bibitem{Kas72} \by B.~S.~Kashin \paper On a property of functional series \jour Mat. Zametki \yr 1972 \vol 11 \issue 5 \pages 481--490 \mathnet{http://mi.mathnet.ru/mz9814} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=304914} \zmath{https://zbmath.org/?q=an:0245.40002|0232.40004} \transl \jour Math. Notes \yr 1972 \vol 11 \issue 5 \pages 294--299 \crossref{https://doi.org/10.1007/BF01158640}