A dimensional result for random self-similar sets
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- by Yan-Yan Liu and Jun Wu PDF
- Proc. Amer. Math. Soc. 130 (2002), 2125-2131 Request permission
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 $a.s.$References
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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
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 2125-2131
- MSC (2000): Primary 60D05; Secondary 28A78
- DOI: https://doi.org/10.1090/S0002-9939-02-06311-6
- MathSciNet review: 1896049