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Porous measures on : Local structure and dimensional properties

Authors:	Esa Jä rvenpä ä Maarit Jä rvenpä ä

Institution:	Department of Mathematics, P.O. Box 35, University of Jyväskylä, FIN-40351 Jyväskylä, Finland ; Department of Mathematics, P.O. Box 35, University of Jyväskylä, FIN-40351 Jyväskylä, Finland

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 as porosity tends to its maximum value.

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