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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 dimensional result for random self-similar sets


Authors: Yan-Yan Liu and Jun Wu
Journal: Proc. Amer. Math. Soc. 130 (2002), 2125-2131
MSC (2000): Primary 60D05; Secondary 28A78
Published electronically: January 17, 2002
MathSciNet review: 1896049
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Abstract: A very important property of a deterministic self-similar set is that its Hausdorff dimension and upper box-counting dimension coincide. This paper considers the random case. We show that for a random self-similar set, its Hausdorff dimension and upper box-counting dimension are equal $a.s.$


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Additional Information

Yan-Yan Liu
Affiliation: Department of Mathematics and Nonlinear Science Center, Wuhan University, Wuhan, Hubei, 430072, People’s Republic of China
Email: lisa-yy@263.net

Jun Wu
Affiliation: Department of Mathematics and Nonlinear Science Center, Wuhan University, Wuhan, Hubei, 430072, People’s Republic of China
Email: wujunyu@public.wh.hb.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06311-6
PII: S 0002-9939(02)06311-6
Keywords: Random self-similar set, Hausdorff dimension, box-counting dimension
Received by editor(s): July 16, 2000
Received by editor(s) in revised form: February 14, 2001
Published electronically: January 17, 2002
Additional Notes: This research was supported by the Special Funds for Major State Basic Research Projects
Communicated by: Claudia M. Neuhauser
Article copyright: © Copyright 2002 American Mathematical Society