Sh. Levental, V. S. Mandrekar, S. A. Chobanyan, “Towards Nikishin's Theorem on the Almost Sure Convergence of Rearrangements of Functional Series”, Funktsional. Anal. i Prilozhen., 45:1 (2011), 41–55; Funct. Anal. Appl., 45:1 (2011), 33

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Funktsional'nyi Analiz i ego Prilozheniya, 2011, Volume 45, Issue 1, Pages 41–55
DOI: https://doi.org/10.4213/faa3026 (Mi faa3026)

This article is cited in 7 scientific papers (total in 7 papers)

Towards Nikishin's Theorem on the Almost Sure Convergence of Rearrangements of Functional Series

Sh. Levental^a, V. S. Mandrekar^a, S. A. Chobanyan^b

^a Michigan State University
^b Muskhelishvili Institute of Computational Mathematics

Full-text PDF (273 kB) Citations (7)

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DOI: https://doi.org/10.4213/faa3026

Abstract: Necessary and sufficient conditions are found for the almost sure convergence of almost all simple rearrangements of a series of Banach space valued random variables. The results go back to Nikishin's well-known theorem on the existence of an almost surely convergent rearrangement of a numerical random series. An example is also given of a numerical random series with general term tending to zero almost surely such that this series converges in probability and any its rearrangement diverges almost surely.

Keywords: rearrangement of a series in a Banach space, almost sure convergence,

${\mathbf k}$ -simple permutation, Nikishin's theorem.

Received: 26.08.2009

English version:
Functional Analysis and Its Applications, 2011, Volume 45, Issue 1, Pages 33–45
DOI: https://doi.org/10.1007/s10688-011-0004-y

Bibliographic databases:

Document Type: Article

UDC: 519.2+517.51+517.98

Language: Russian

Citation: Sh. Levental, V. S. Mandrekar, S. A. Chobanyan, “Towards Nikishin's Theorem on the Almost Sure Convergence of Rearrangements of Functional Series”, Funktsional. Anal. i Prilozhen., 45:1 (2011), 41–55; Funct. Anal. Appl., 45:1 (2011), 33–45

Citation in format AMSBIB

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https://doi.org/10.4213/faa3026

https://www.mathnet.ru/eng/faa/v45/i1/p41

This publication is cited in the following 7 articles:

Sergei Chobanyan, Shlomo Levental, “Maximum inequalities in rearrangements of orthogonal series”, Georgian Mathematical Journal, 29:6 (2022), 823
Mukeru S., “On the Convergence of Series of Dependent Random Variables”, J. Theor. Probab., 34:3 (2021), 1299–1320
Charatonik W.J., Samulewicz A., Witula R., “Limit sets in normed linear spaces”, Colloq. Math., 147:1 (2017), 35–42
S. Chobanyan, G. Giorgobiani, V. Kvaratskhelia, Sh. Levental, V. Tarieladze, “On rearrangement theorems in Banach spaces”, Georgian Math. J., 21:2 (2014), 157–163
Theory Probab. Appl., 59:4 (2015), 677–684
Chobanyan S., Levental S., “Contraction principle for tail probabilities of sums of exchangeable random vectors with multipliers”, Statist. Probab. Lett., 83:7 (2013), 1720–1724
Chobanyan S., Leyental S., Mandrekar V., “Almost surely convergent summands of a random sum”, Statist. Probab. Lett., 82:1 (2012), 212–216

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

Functional Analysis and Its Applications

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Abstract page:	569
Full-text PDF :	287
References:	108
First page:	5

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