On intersections of Cantor sets: Hausdorff measure

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.

Bibliographic Details
Main Authors:	Steen Pedersen, Jason D. Phillips
Format:	Article
Language:	English
Published:	AGH Univeristy of Science and Technology Press 2013-01-01
Series:	Opuscula Mathematica
Subjects:	Hausdorff measure fractal Cantor set translation intersection digit expansion
Online Access:	http://www.opuscula.agh.edu.pl/vol33/3/art/opuscula_math_3331.pdf

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spelling	doaj-b722b6b653984b5c8a352631bc241a502020-11-24T23:46:03ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742013-01-01333575598http://dx.doi.org/10.7494/OpMath.2013.33.3.5753331On intersections of Cantor sets: Hausdorff measureSteen Pedersen0Jason D. Phillips1Wright State University, Department of Mathematics, Dayton OH 45435Wright State University, Department of Mathematics, Dayton OH 45435We 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.http://www.opuscula.agh.edu.pl/vol33/3/art/opuscula_math_3331.pdfHausdorff measurefractalCantor settranslationintersectiondigit expansion
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Steen Pedersen Jason D. Phillips
spellingShingle	Steen Pedersen Jason D. Phillips On intersections of Cantor sets: Hausdorff measure Opuscula Mathematica Hausdorff measure fractal Cantor set translation intersection digit expansion
author_facet	Steen Pedersen Jason D. Phillips
author_sort	Steen Pedersen
title	On intersections of Cantor sets: Hausdorff measure
title_short	On intersections of Cantor sets: Hausdorff measure
title_full	On intersections of Cantor sets: Hausdorff measure
title_fullStr	On intersections of Cantor sets: Hausdorff measure
title_full_unstemmed	On intersections of Cantor sets: Hausdorff measure
title_sort	on intersections of cantor sets: hausdorff measure
publisher	AGH Univeristy of Science and Technology Press
series	Opuscula Mathematica
issn	1232-9274
publishDate	2013-01-01
description	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.
topic	Hausdorff measure fractal Cantor set translation intersection digit expansion
url	http://www.opuscula.agh.edu.pl/vol33/3/art/opuscula_math_3331.pdf
work_keys_str_mv	AT steenpedersen onintersectionsofcantorsetshausdorffmeasure AT jasondphillips onintersectionsofcantorsetshausdorffmeasure
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On intersections of Cantor sets: Hausdorff measure

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