Illinois Journal of Mathematics

Upper porous measures on metric spaces

Ville Suomala

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We show how a standard method of geometric measure theory for providing density estimates may be used in general metric spaces to obtain information on the upper porosity of packing type measures. We also obtain a connection between lower densities and the upper porosity of measures on Euclidean spaces.

Article information

Illinois J. Math., Volume 52, Number 3 (2008), 967-980.

First available in Project Euclid: 1 October 2009

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Zentralblatt MATH identifier

Primary: 28A78: Hausdorff and packing measures
Secondary: 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05] 28A12: Contents, measures, outer measures, capacities


Suomala, Ville. Upper porous measures on metric spaces. Illinois J. Math. 52 (2008), no. 3, 967--980. doi:10.1215/ijm/1254403725.

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