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Packing dimension of mean porous measures

Abstract:

We prove that the packing dimension of any mean porous Radon measure on $\mathbb R^d$ may be estimated from above by a function which depends on mean porosity. The upper bound tends to $d-1$ as mean porosity tends to its maximum value. This result was stated in \cite{BS}, and in a weaker form in \cite{JJ1}, but the proofs are not correct. Quite surprisingly, it turns out that mean porous measures are not necessarily approximable by mean porous sets. We verify this by constructing an example o...

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Publication status:
Published

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Publisher copy:
10.1112/jlms/jdp040

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Journal:
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
Volume:
80
Issue:
2
Pages:
514-530
Publication date:
2007-05-16
DOI:
EISSN:
1469-7750
ISSN:
0024-6107
Source identifiers:
190359
Language:
English
Keywords:
Pubs id:
pubs:190359
UUID:
uuid:a0b14aee-2ade-498d-a7ac-3643616c2cdd
Local pid:
pubs:190359
Deposit date:
2012-12-19

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