### Dimensions of intersections and distance sets for polyhedral norms.

K. J. Falconer
Source: Real Anal. Exchange Volume 30, Number 2 (2004), 719- 726 .

#### Abstract

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.

First Page:
Primary Subjects: 28A78, 28A12, 28A80, 51F99
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.rae/1129416466
Mathematical Reviews number (MathSciNet): MR2177429
Zentralblatt MATH identifier: 1107.28008

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