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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. Leventala, V. S. Mandrekara, S. A. Chobanyanb

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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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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