Opuscula Mathematica
Opuscula Math. 33, no. 3 (2013), 575-598

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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Steen Pedersen
Wright State University, Department of Mathematics, Dayton OH 45435
Jason D. Phillips
Wright State University, Department of Mathematics, Dayton OH 45435
About the article ▼
Received: 2012-12-18.
Revised: 2013-01-03.
Accepted: 2013-01-06.
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Steen Pedersen, Jason D. Phillips, On intersections of Cantor sets: Hausdorff measure, Opuscula Math. 33, no. 3 (2013), 575-598, http://dx.doi.org/10.7494/OpMath.2013.33.3.575.
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