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On the Hausdorff dimensions of distance sets

Published online by Cambridge University Press:  26 February 2010

K. J. Falconer
Affiliation:
School of Mathematics, University Walk, Bristol, BS8 1TW
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Extract

If E is a subset of ℝn (n ≥ 1) we define the distance set of E as

The best known result on distance sets is due to Steinhaus [11], namely, that, if E ⊂ ℝn is measurable with positive n-dimensional Lebesgue measure, then D(E) contains an interval [0, ε) for some ε > 0. A number of variations of this have been examined, see Falconer [6, p. 108] and the references cited therein.

Type
Research Article
Copyright
Copyright © University College London 1985

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