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ISSN 1079-6762

 

Thickness measures for Cantor sets


Author: S. Astels
Journal: Electron. Res. Announc. Amer. Math. Soc. 5 (1999), 108-111
MSC (1991): Primary 58F12; Secondary 28A78
Published electronically: July 20, 1999
MathSciNet review: 1701889
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Abstract: For a fixed $k\ge 1$ let $C_1,\dots,C_k$ be generalized Cantor sets. We examine various criteria under which $C_1+\dots + C_k$ contains an interval. When these criteria do not hold, we give a lower bound for the Hausdorff dimension of $C_1+\dots+C_k$. Our work will involve the development of two different types of thickness measures.


References [Enhancements On Off] (What's this?)

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Additional Information

S. Astels
Affiliation: Department of Pure Mathematics, The University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Email: sastels@barrow.uwaterloo.ca

DOI: http://dx.doi.org/10.1090/S1079-6762-99-00068-2
PII: S 1079-6762(99)00068-2
Keywords: Cantor sets, sums of sets, Hausdorff dimension
Received by editor(s): March 15, 1999
Published electronically: July 20, 1999
Additional Notes: Research supported in part by the Natural Sciences and Engineering Research Council of Canada.
Communicated by: Yitzhak Katznelson
Article copyright: © Copyright 1999 American Mathematical Society