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Mathematics of the USSR-Sbornik, 1974, Volume 23, Issue 4, Pages 509–519
DOI: https://doi.org/10.1070/SM1974v023n04ABEH002183
(Mi sm3732)
 

This article is cited in 3 scientific papers (total in 3 papers)

On unconditional convergence in the space $L_1$

B. S. Kashin
References:
Abstract: The paper contains a proof of the following
Theorem. {\it Suppose $\sum_{k=1}^\infty f_k(x)$ converges unconditionally in $L_1[0,1]$. Then for any $\varepsilon>0$ there exists a set $E_\varepsilon\subset[0,1],$ $\mu E_\varepsilon>1-\varepsilon,$ such that $\sum_{k=1}^\infty f_k(x)$ converges unconditionally in $L_q(E_\varepsilon)$ for every $q<2$.}
This result is obtained as a corollary of a more general theorem.
Bibliography: 2 titles.
Received: 14.06.1973
Bibliographic databases:
Document Type: Article
UDC: 517.52
MSC: 40A05, 46E30
Language: English
Original paper language: Russian
Citation: B. S. Kashin, “On unconditional convergence in the space $L_1$”, Math. USSR-Sb., 23:4 (1974), 509–519
Citation in format AMSBIB
\Bibitem{Kas74}
\by B.~S.~Kashin
\paper On unconditional convergence in the space~$L_1$
\jour Math. USSR-Sb.
\yr 1974
\vol 23
\issue 4
\pages 509--519
\mathnet{http://mi.mathnet.ru//eng/sm3732}
\crossref{https://doi.org/10.1070/SM1974v023n04ABEH002183}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=385537}
\zmath{https://zbmath.org/?q=an:0321.28005}
Linking options:
  • https://www.mathnet.ru/eng/sm3732
  • https://doi.org/10.1070/SM1974v023n04ABEH002183
  • https://www.mathnet.ru/eng/sm/v136/i4/p540
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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