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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Dimension functions of Cantor sets


Authors: Ignacio Garcia, Ursula Molter and Roberto Scotto
Journal: Proc. Amer. Math. Soc. 135 (2007), 3151-3161
MSC (2000): Primary 28A78, 28A80
Published electronically: June 21, 2007
MathSciNet review: 2322745
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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.


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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: http://dx.doi.org/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
Published electronically: June 21, 2007
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.