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2004-2005 Dimensions of intersections and distance sets for polyhedral norms.
K. J. Falconer
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Real Anal. Exchange 30(2): 719-726 (2004-2005).


We obtain an estimate for the typical Hausdorff dimension of the intersection of a set $E$ with homothetic copies of a set $F$, where $E$ and $F$ are Borel subsets of $\mathbb{R}^{n}$. We apply this to the `distance set problem' for a polyhedral norm on $\mathbb{R}^{n}$, by showing that there are subsets of full dimension with distance set of Lebesgue measure 0.


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K. J. Falconer. "Dimensions of intersections and distance sets for polyhedral norms.." Real Anal. Exchange 30 (2) 719 - 726, 2004-2005.


Published: 2004-2005
First available in Project Euclid: 15 October 2005

zbMATH: 1107.28008
MathSciNet: MR2177429

Primary: 28A12 , 28A78 , 28A80 , 51F99

Keywords: distance set , Hausdorff dimension , intersection

Rights: Copyright © 2004 Michigan State University Press

Vol.30 • No. 2 • 2004-2005
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