A law of large numbers for arithmetic functions

Authors:
Katusi Fukuyama and Yutaka Komatsu

Journal:
Proc. Amer. Math. Soc. **137** (2009), 349-352

MSC (2000):
Primary 60F15, 11A25; Secondary 60G50

Published electronically:
August 15, 2008

MathSciNet review:
2439459

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

**Katusi Fukuyama**

Affiliation:
Department of Mathematics, Kobe University, Rokko, Kobe, 657-8501 Japan

Email:
fukuyama@math.kobe-u.ac.jp

**Yutaka Komatsu**

Affiliation:
Graduate School of Science and Technology, Kobe University, Rokko, Kobe, 657-8501 Japan

DOI:
http://dx.doi.org/10.1090/S0002-9939-08-09517-8

Keywords:
Strong law of large numbers,
strongly additive functions

Received by editor(s):
November 5, 2007

Received by editor(s) in revised form:
December 17, 2007, and January 13, 2008

Published electronically:
August 15, 2008

Additional Notes:
The first author was supported in part by Grant-in-Aid for Scientific Research (B) 17340029 from the Japan Society for the Promotion of Sciences.

Communicated by:
Richard C. Bradley

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.