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

 

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: 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
PII: S 0002-9939(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.