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.
- Steen Pedersen
- Wright State University, Department of Mathematics, Dayton OH 45435
- Jason D. Phillips
- Wright State University, Department of Mathematics, Dayton OH 45435
- Received: 2012-12-18.
- Revised: 2013-01-03.
- Accepted: 2013-01-06.
