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Proceedings of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0002-9939-99-05107-2
Published electronically: May 13, 1999
MathSciNet review: 1637408
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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