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Mat. Zametki, 1973, Volume 14, Issue 5, Pages 645–654 (Mi mz9949)  

This article is cited in 8 scientific papers (total in 8 papers)

Stability of unconditional convergence almost everywhere

B. S. Kashin

Moscow State University

Abstract: We will investigate the properties of series of functions which are unconditionally convergent almost everywhere on $[0, 1]$. We will establish the following theorem: If the series $\sum_{k=1}^\infty f_k(x)$ converges unconditionally almost everywhere, then there exists a sequence $\{\beta_k\}_1^\infty$, $\beta_k\uparrow\infty$ such that if $\lambda_k\leqslant\beta_k$, $k=1,2,…$, the series $\sum_{k=1}^\infty\lambda_k f_k(x)$ converges unconditionally almost everywhere.

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English version:
Mathematical Notes, 1973, 14:5, 930–935

Bibliographic databases:

UDC: 517.5
Received: 21.03.1973

Citation: B. S. Kashin, “Stability of unconditional convergence almost everywhere”, Mat. Zametki, 14:5 (1973), 645–654; Math. Notes, 14:5 (1973), 930–935

Citation in format AMSBIB
\Bibitem{Kas73}
\by B.~S.~Kashin
\paper Stability of unconditional convergence almost everywhere
\jour Mat. Zametki
\yr 1973
\vol 14
\issue 5
\pages 645--654
\mathnet{http://mi.mathnet.ru/mz9949}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=330400}
\zmath{https://zbmath.org/?q=an:0283.40002}
\transl
\jour Math. Notes
\yr 1973
\vol 14
\issue 5
\pages 930--935
\crossref{https://doi.org/10.1007/BF01462252}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Labuda I., “Bounded Multiplier Convergence of Series in Orlicz Spaces”, 23, no. 6, 1975, 651–655  mathscinet  zmath  isi
    2. Turpin P., “Summable Sequences in Some Spaces of Measurable Functions”, 280, no. 6, 1975, 349–352  zmath  isi
    3. Turpin P., “Non-Bounded Vector-Valued Measure”, 280, no. 8, 1975, 509–511  zmath  isi
    4. Kalton N., Peck N., Roberts J., “Lo-Valued Vector Measures Are Bounded”, Proc. Amer. Math. Soc., 85:4 (1982), 575–582  crossref  mathscinet  zmath  isi
    5. Diestel J., Uhl J., “Progress in Vector Measures - 1977-83”, Lect. Notes Math., 1033 (1983), 144–192  crossref  mathscinet  zmath  isi
    6. Hu T., Nam E., Rosalsky A., Volodin A., “An Application of the Ryll-Nardzewski-Woyczynski Theorem to a Uniform Weak Law For Tail Series of Weighted Sums of Random Elements in Banach Spaces”, Stat. Probab. Lett., 48:4 (2000), 369–374  crossref  mathscinet  zmath  isi
    7. Thomas E.G.F., “Vector Integration”, Quaest. Math., 35:4 (2012), 391–416  crossref  mathscinet  zmath  isi  scopus
    8. Drewnowski L., Labuda I., “Bartle-Dunford-Schwartz Integration”, J. Math. Anal. Appl., 401:2 (2013), 620–640  crossref  mathscinet  zmath  isi  scopus
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