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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Regularly varying sequences


Authors: J. Galambos and E. Seneta
Journal: Proc. Amer. Math. Soc. 41 (1973), 110-116
MSC: Primary 26A12
MathSciNet review: 0323963
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Abstract: A simple necessary and sufficient condition is developed for a sequence $ \{ \theta (n)\} ,n = 0,1,2, \cdots $, of positive terms, to satisfy $ \theta (n) = R(n),n \geqq 0$, where $ R( \cdot )$ is a regularly varying function on $ [0,\infty )$. The condition (2.1), below, leads to a Karamata-type exponential representation for $ \theta (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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DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0323963-5
PII: S 0002-9939(1973)0323963-5
Keywords: Regularly varying functions, regularly varying sequences, imbedding sequences in functions, exponential representations of sequences and functions
Article copyright: © Copyright 1973 American Mathematical Society