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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Porous measures on $\mathbb{R}^{n}$: Local structure and dimensional properties


Authors: Esa Järvenpää and Maarit Järvenpää
Journal: Proc. Amer. Math. Soc. 130 (2002), 419-426
MSC (2000): Primary 28A12, 28A80
Published electronically: June 8, 2001
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Abstract:

We study dimensional properties of porous measures on $\mathbb{R}^{n}$. As a corollary of a theorem describing the local structure of nearly uniformly porous measures we prove that the packing dimension of any Radon measure on $\mathbb{R}^{n}$ has an upper bound depending on porosity. This upper bound tends to $n-1$ as porosity tends to its maximum value.


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Additional Information

Esa Järvenpää
Affiliation: Department of Mathematics, P.O. Box 35, University of Jyväskylä, FIN-40351 Jyväskylä, Finland
Email: esaj@math.jyu.fi

Maarit Järvenpää
Affiliation: Department of Mathematics, P.O. Box 35, University of Jyväskylä, FIN-40351 Jyväskylä, Finland
Email: amj@math.jyu.fi

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06161-5
PII: S 0002-9939(01)06161-5
Received by editor(s): June 13, 2000
Published electronically: June 8, 2001
Communicated by: David Preiss
Article copyright: © Copyright 2001 American Mathematical Society