A measure theoretical subsequence characterization of statistical convergence
Harry I. Miller
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Source: Crossref
Published: Jan 1, 1995
DOI: 10.1090/s0002-9947-1995-1260176-6
Open original source ↗Source 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 A in place of C 1 {C_1} . The main result in this paper is a theorem that gives meaning to the statement: S = { s n } S = \{ {s_n}\} converges to L L statistically ( T ) (T) if and only if "most" of the subsequences of S S converge, in the ordinary sense, to L L . Here T 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.
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