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Thickness measures for Cantor sets
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## Thickness measures for Cantor sets

### S. Astels

**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.

*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.

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