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Matematicheskie Zametki, 1975, Volume 18, Issue 1, Pages 129–135 (Mi mzm7634)  

This article is cited in 20 scientific papers (total in 21 papers)

An extension of the Lindeberg–Feller theorem

V. I. Rotar'

Central Economics and Mathematics Institute, Academy of Sciences of the USSR
Abstract: A new version is presented of the necessary and sufficient condition of convergence, to a normal law, of sums of independent variables in a nonclassical situation (i.e., absence of limiting negligibility of variables). The obtained condition differs from previously obtained conditions by the fact that it does not use Levy's metric and that is is closer to classical formulations. A similar condition is sufficient for the closeness of two convolutions when the number of components of the convolutions increases without bounds.
Received: 10.11.1974
English version:
Mathematical Notes, 1975, Volume 18, Issue 1, Pages 660–663
DOI: https://doi.org/10.1007/BF01461150
Bibliographic databases:
UDC: 519.21.9
Language: Russian
Citation: V. I. Rotar', “An extension of the Lindeberg–Feller theorem”, Mat. Zametki, 18:1 (1975), 129–135; Math. Notes, 18:1 (1975), 660–663
Citation in format AMSBIB
\Bibitem{Rot75}
\by V.~I.~Rotar'
\paper An extension of the Lindeberg--Feller theorem
\jour Mat. Zametki
\yr 1975
\vol 18
\issue 1
\pages 129--135
\mathnet{http://mi.mathnet.ru/mzm7634}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=400348}
\zmath{https://zbmath.org/?q=an:0348.60025}
\transl
\jour Math. Notes
\yr 1975
\vol 18
\issue 1
\pages 660--663
\crossref{https://doi.org/10.1007/BF01461150}
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  • https://www.mathnet.ru/eng/mzm/v18/i1/p129
  • This publication is cited in the following 21 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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