Regularly Varying Sequences

摘要

A simple necessary and sufficient condition is developed for a sequence (theta(n)) , n = 0,1,2,.... of positive terms, to satisfy theta(n) = R(n), n > or = 0 , where R(.) is a regularly varying function on (0, infinity). The condition given in the report 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. (Author)