MATHEMATICA BOHEMICA, Vol. 126, No. 1, pp. 191-208 (2001)

Statistical convergence of subsequences
of a given sequence

M. Macaj, T. Salat

M. Macaj, T. Salat, Comenius University, Department of Algebra and Number Theory, Mlynska dolina, 842 15 Bratislava, Slovakia, e-mail: Martin.Macaj@fmph.uniba.sk

Abstract: 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.

Keywords: asymptotic density, statistical convergence, Lebesgue measure, Hausdorff dimension, Baire category

Classification (MSC2000): 40A05, 18B05, 11K55

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