Sum of Cantor sets: Self-similarity and measure

Author:
Pedro Mendes

Journal:
Proc. Amer. Math. Soc. **127** (1999), 3305-3308

MSC (1991):
Primary 28A78, 58F14

Published electronically:
May 13, 1999

MathSciNet review:
1637408

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Abstract | References | Similar Articles | Additional Information

Abstract: In this note it is shown that the sum of two homogeneous Cantor sets is often a uniformly contracting self-similar set and it is given a sufficient condition for such a set to be of Lebesgue measure zero (in fact, of Hausdorff dimension less than one and positive Hausdorff measure at this dimension).

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Additional Information

**Pedro Mendes**

Affiliation:
Departamento de Matemática, ICEx, UFMG Av. Antonio Carlos 6627 31270.901 Belo Horizonte, MG, Brazil

Email:
pmendes@mat.ufmg.br

DOI:
https://doi.org/10.1090/S0002-9939-99-05107-2

Keywords:
Self-similar set,
homogeneous Cantor set,
Hausdorff dimension,
Hausdorff measure

Received by editor(s):
February 6, 1998

Published electronically:
May 13, 1999

Communicated by:
Michael Handel

Article copyright:
© Copyright 1999
American Mathematical Society