A measure theoretical subsequence characterization of statistical convergence

Author:
Harry I. Miller

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

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Abstract | References | Similar Articles | Additional Information

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 in place of .

The main result in this paper is a theorem that gives meaning to the statement: converges to statistically if and only if "most" of the subsequences of converge, in the ordinary sense, to . Here 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.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1995-1260176-6

Article copyright:
© Copyright 1995
American Mathematical Society