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).References
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Additional Information
- Katusi Fukuyama
- Affiliation: Department of Mathematics, Kobe University, Rokko, Kobe, 657-8501 Japan
- MR Author ID: 256708
- Email: fukuyama@math.kobe-u.ac.jp
- Yutaka Komatsu
- Affiliation: Graduate School of Science and Technology, Kobe University, Rokko, Kobe, 657-8501 Japan
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 349-352
- MSC (2000): Primary 60F15, 11A25; Secondary 60G50
- DOI: https://doi.org/10.1090/S0002-9939-08-09517-8
- MathSciNet review: 2439459