Packing dimension of mean porous measures

Beliaev, Dmitry; Järvenpää, E.; Järvenpää, M.; Käenmäki, A.; Rajala, T.; Smirnov, Stanislav; Suomala, V.

doi:10.1112/jlms/jdp040

Scientific article

English

Packing dimension of mean porous measures

Contributors

Beliaev, Dmitry; Järvenpää, E.; Järvenpää, M.; Käenmäki, A.; Rajala, T.; Smirnov, Stanislav; Suomala, V.

Published in

Journal of the London Mathematical Society, vol. 80, no. 2, p. 514-530

Publication date

2009

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 of a mean porous measure $mu$ on $mathbb R$ such that $mu(A)=0$ for all mean porous sets $Asubsetmathbb R$.

Classification

arxiv : math.CA

Note

Revised version

UNIGE affiliation entities

Faculté des sciences / Section de mathématiques

Citation (ISO format)

BELIAEV, Dmitry et al. Packing dimension of mean porous measures. In: Journal of the London Mathematical Society, 2009, vol. 80, n° 2, p. 514–530. doi: 10.1112/jlms/jdp040

Article

Identifiers

PID : unige:8527
DOI : 10.1112/jlms/jdp040
arXiv : 0705.2447

Journal ISSN

0024-6107

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02/07/2010 09:22:00

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14/03/2023 15:49:40

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Packing dimension of mean porous measures

Contributors

Published in

Publication date

Abstract

Classification

Note

UNIGE affiliation entities

Citation (ISO format)

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Journal ISSN

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Creation

First validation

Update

Status update

Last indexation