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

 

Classifying Cantor sets by their fractal dimensions


Authors: Carlos A. Cabrelli, Kathryn E. Hare and Ursula M. Molter
Journal: Proc. Amer. Math. Soc. 138 (2010), 3965-3974
MSC (2010): Primary 28A78, 28A80
Published electronically: May 14, 2010
MathSciNet review: 2679618
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Abstract: In this article we study Cantor sets defined by monotone sequences, in the sense of Besicovich and Taylor. We classify these Cantor sets in terms of their $ h$-Hausdorff and $ h$-packing measures, for the family of dimension functions $ h$, and characterize this classification in terms of the underlying sequences.


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Additional Information

Carlos A. Cabrelli
Affiliation: Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria, C1428EGA C.A.B.A., Argentina – and – CONICET, Argentina
Email: cabrelli@dm.uba.ar

Kathryn E. Hare
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, ON, Canada
Email: kehare@uwaterloo.edu

Ursula M. Molter
Affiliation: Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria, C1428EGA C.A.B.A., Argentina – and – CONICET, Argentina
Email: umolter@dm.uba.ar

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10396-9
PII: S 0002-9939(2010)10396-9
Keywords: Hausdorff dimension, packing dimension, Cantor set, cut-out set
Received by editor(s): May 11, 2009
Received by editor(s) in revised form: January 15, 2010
Published electronically: May 14, 2010
Additional Notes: The first and third authors were partially supported by Grants UBACyT X149 and X028 (UBA), PICT 2006-00177 (ANPCyT), and PIP 112-200801-00398 (CONICET)
The second author was partially supported by NSERC
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2010 American Mathematical Society