Real Analysis Exchange

Dimensions of intersections and distance sets for polyhedral norms.

K. J. Falconer

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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.

Article information

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

Dates
First available in Project Euclid: 15 October 2005

Permanent link to this document
http://projecteuclid.org/euclid.rae/1129416466

Mathematical Reviews number (MathSciNet)
MR2177429

Zentralblatt MATH identifier
1107.28008

Subjects
Primary: 28A78: Hausdorff and packing measures 28A12: Contents, measures, outer measures, capacities 28A80: Fractals [See also 37Fxx] 51F99: None of the above, but in this section

Keywords
Hausdorff dimension intersection distance set

Citation

Falconer, K. J. Dimensions of intersections and distance sets for polyhedral norms. Real Anal. Exchange 30 (2004), no. 2, 719-- 726. http://projecteuclid.org/euclid.rae/1129416466.


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