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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A measure theoretical subsequence characterization of statistical convergence
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by Harry I. Miller PDF
Trans. Amer. Math. Soc. 347 (1995), 1811-1819 Request permission

Abstract:

The concept of statistical convergence of a sequence was first introduced by H. Fast. Statistical convergence was generalized by R. C. Buck, and studied by other authors, using a regular nonnegative summability matrix $A$ in place of ${C_1}$. The main result in this paper is a theorem that gives meaning to the statement: $S = \{ {s_n}\}$ converges to $L$ statistically $(T)$ if and only if "most" of the subsequences of $S$ converge, in the ordinary sense, to $L$. Here $T$ is a regular, nonnegative and triangular matrix. Corresponding results for lacunary statistical convergence, recently defined and studied by J. A. Fridy and C. Orhan, are also presented.
References
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 1811-1819
  • MSC: Primary 40C05; Secondary 40A99, 40D25
  • DOI: https://doi.org/10.1090/S0002-9947-1995-1260176-6
  • MathSciNet review: 1260176