Abstract
In this correspondence, we prove that if X is a random variable with P(X=0)=0 and E|X|=∞, then there exists a continuous function G on (0,∞) with 0<G(x)↑∞ and xG(x)↑∞ as 0<x↑∞ such that E(|X|/G(|X|))=∞. An application of this result pertaining to the Kolmogorov strong law of large numbers is established.
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