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

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

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
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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
2. Turpin P., “Summable Sequences in Some Spaces of Measurable Functions”, 280, no. 6, 1975, 349–352
3. Turpin P., “Non-Bounded Vector-Valued Measure”, 280, no. 8, 1975, 509–511
4. Kalton N., Peck N., Roberts J., “Lo-Valued Vector Measures Are Bounded”, Proc. Amer. Math. Soc., 85:4 (1982), 575–582
5. Diestel J., Uhl J., “Progress in Vector Measures - 1977-83”, Lect. Notes Math., 1033 (1983), 144–192
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
7. Thomas E.G.F., “Vector Integration”, Quaest. Math., 35:4 (2012), 391–416
8. Drewnowski L., Labuda I., “Bartle-Dunford-Schwartz Integration”, J. Math. Anal. Appl., 401:2 (2013), 620–640
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