Opuscula Math. 33, no. 3 (2013), 575-598
http://dx.doi.org/10.7494/OpMath.2013.33.3.575

Opuscula Mathematica

On intersections of Cantor sets: Hausdorff measure

Steen Pedersen
Jason D. Phillips

Abstract. We establish formulas for bounds on the Haudorff measure of the intersection of certain Cantor sets with their translates. As a consequence we obtain a formula for the Hausdorff dimensions of these intersections.

Keywords: Hausdorff measure, fractal, Cantor set, translation, intersection, digit expansion.

Mathematics Subject Classification: 11K55, 28A78, 28A80, 37F99.

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