## 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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*Lacunary statistical summability*(to appear).

## 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