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Regularly Varying Sequences

J. Galambos and E. Seneta
Proceedings of the American Mathematical Society
Vol. 41, No. 1 (Nov., 1973), pp. 110-116
DOI: 10.2307/2038824
Stable URL: http://www.jstor.org/stable/2038824
Page Count: 7
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Regularly Varying Sequences
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Abstract

A simple necessary and sufficient condition is developed for a sequence {θ(n)}, n = 0, 1, 2,⋯, of positive terms, to satisfy θ(n) = R(n), n ≥ 0, where R(·) is a regularly varying function on [ 0, ∞). The condition (2.1), below, leads to a Karamata-type exponential representation for θ(n). Various associated difficulties are also discussed. (The results are of relevance in connection with limit theorems in various branches of probability theory.)

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