Real Analysis Exchange

Dimensions of intersections and distance sets for polyhedral norms.

K. J. Falconer

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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

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

First available: 15 October 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Hausdorff dimension intersection distance set


Falconer, K. J. Dimensions of intersections and distance sets for polyhedral norms. Real Analysis Exchange 30 (2004), no. 2, 719-- 726.

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