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On the Hausdorff dimensions of distance sets

Part of: Classical measure theory

Published online by Cambridge University Press:  26 February 2010

K. J. Falconer
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.

MSC classification

Secondary: 28A75: Length, area, volume, other geometric measure theory
Type
Research Article
Information
Mathematika , Volume 32 , Issue 2 , December 1985 , pp. 206 - 212
Copyright
Copyright © University College London 1985

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References

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