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Generalizing results of Schatte [11] and Atlagh and Weber [2], in this paper we give conditions for a sequence of random variables to satisfy the almost sure central limit theorem along a given sequence of integers.

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., and Parsons , T. D . On monotone subsequences . Amer. Math. Monthly 95 , 1 ( 1988 ), 44 – 45 . [7] Stroyan , K. D ., and Luxemburg , W. A. J . Introduction to the theory of infinitesimals . Academic Press , New York

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