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The dimension of weakly mean porous measures: a probabilistic approach

Shmerkin, P (2012) The dimension of weakly mean porous measures: a probabilistic approach International Mathematics Research Notices, 2012 (9). pp. 2010-2033.

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Using probabilistic ideas, we prove that the packing dimension of a mean porous measure is strictly smaller than the dimension of the ambient space. Moreover, we give an explicit bound for the packing dimension, which is asymptotically sharp in the case of small porosity. This result was stated in [D. B. Beliaev and S. K. Smirnov, "On dimension of porous measures", Math. Ann. 323 (2002) 123-141], but the proof given there is not correct. We also give estimates on the dimension of weakly mean porous measures, which improve another result of Beliaev and Smirnov.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Shmerkin, P
Date : 2012
DOI : 10.1093/imrn/rnr085
Related URLs :
Additional Information : This is a pre-copy-editing, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The definitive publisher-authenticated version International Mathematics Research Notices 2012, 2012(9): 2010-2033 is available online at International Mathematics Research Notices website.
Depositing User : Symplectic Elements
Date Deposited : 24 Aug 2012 14:13
Last Modified : 31 Oct 2017 14:19

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