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Dimension functions of Cantor sets
Author(s):
Ignacio
Garcia;
Ursula
Molter;
Roberto
Scotto
Journal:
Proc. Amer. Math. Soc.
135
(2007),
3151-3161.
MSC (2000):
Primary 28A78, 28A80
Posted:
June 21, 2007
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Abstract:
We estimate the packing measure of Cantor sets associated to non-increasing sequences through their decay. This result, dual to one obtained by Besicovitch and Taylor, allows us to characterize the dimension functions recently found by Cabrelli et al for these sets.
References:
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Additional Information:
Ignacio
Garcia
Affiliation:
Departamento de Matemática, Facultad de Ingeniería Química, Universidad Nacional del Litoral, Santa Fe, Argentina and IMAL CONICET UNL
Email:
igarcia@math.unl.edu.ar
Ursula
Molter
Affiliation:
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Capital Federal, Argentina and CONICET, Argentina
Email:
umolter@dm.uba.ar
Roberto
Scotto
Affiliation:
Departamento de Matemática, Universidad Nacional del Litoral, Santa Fe, Argentina
Email:
scotto@math.unl.edu.ar
DOI:
10.1090/S0002-9939-07-09019-3
PII:
S 0002-9939(07)09019-3
Keywords:
Cantor sets,
packing measure,
Hausdorff dimension,
dimension function
Received by editor(s):
May 2, 2006
Posted:
June 21, 2007
Communicated by:
Michael T. Lacey
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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