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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
DOI:
https://doi.org/10.1090/S1079-6762-99-00068-2
Published electronically:
July 20, 1999
MathSciNet review:
1701889
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
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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
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