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Sum of Cantor sets: Self-similarity and measure
Author(s):
Pedro
Mendes
Journal:
Proc. Amer. Math. Soc.
127
(1999),
3305-3308.
MSC (1991):
Primary 28A78, 58F14
Posted:
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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- 3.
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- 4.
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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:
10.1090/S0002-9939-99-05107-2
PII:
S 0002-9939(99)05107-2
Keywords:
Self-similar set,
homogeneous Cantor set,
Hausdorff dimension,
Hausdorff measure
Received by editor(s):
February 6, 1998
Posted:
May 13, 1999
Communicated by:
Michael Handel
Copyright of article:
Copyright
1999,
American Mathematical Society
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