Porous measures on $\mathbb {R}^{n}$: Local structure and dimensional properties
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- by Esa Järvenpää and Maarit Järvenpää PDF
- Proc. Amer. Math. Soc. 130 (2002), 419-426 Request permission
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.References
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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
- Received by editor(s): June 13, 2000
- Published electronically: June 8, 2001
- Communicated by: David Preiss
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 419-426
- MSC (2000): Primary 28A12, 28A80
- DOI: https://doi.org/10.1090/S0002-9939-01-06161-5
- MathSciNet review: 1862121