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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.

Copyright 1999 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 05 (1999), pp. 108-111
• Publisher Identifier: S 1079-6762(99)00068-2
• 1991 Mathematics Subject Classification. Primary 58F12; Secondary 28A78
• Key words and phrases. Cantor sets, sums of sets, Hausdorff dimension
• Received by the editors March 15, 1999
• Posted on July 20, 1999
• Communicated by Yitzhak Katznelson
• Comments (When Available)

S. Astels

Department of Pure Mathematics, The University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

E-mail address: sastels@barrow.uwaterloo.ca

Research supported in part by the Natural Sciences and Engineering Research Council of Canada.