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Keywords:
asymptotic density; statistical convergence; Lebesgue measure; Hausdorff dimension; Baire category
asymptotic density; statistical convergence; Lebesgue measure; Hausdorff dimension; Baire category
Summary:
This paper is closely related to the paper of Harry I. Miller: Measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc. 347 (1995), 1811–1819 and contains a general investigation of statistical convergence of subsequences of an arbitrary sequence from the point of view of Lebesgue measure, Hausdorff dimensions and Baire’s categories.
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