A law of large numbers for arithmetic functions

Fukuyama, Katusi; Komatsu, Yutaka

doi:10.1090/S0002-9939-08-09517-8

A law of large numbers for arithmetic functions
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by Katusi Fukuyama and Yutaka Komatsu PDF

Proc. Amer. Math. Soc. 137 (2009), 349-352 Request permission

Abstract:

We prove the weighted strong law of large numbers for every integrable i.i.d. sequence where the weights are given by a positive strongly additive function satisfying the Lindeberg condition. This result solves one of the open problems raised in the paper by Berkes and Weber (2007).

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