Classifying Cantor sets by their fractal dimensions
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- by Carlos A. Cabrelli, Kathryn E. Hare and Ursula M. Molter PDF
- Proc. Amer. Math. Soc. 138 (2010), 3965-3974 Request permission
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.References
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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
- MR Author ID: 308374
- ORCID: 0000-0002-6473-2636
- Email: cabrelli@dm.uba.ar
- Kathryn E. Hare
- Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, ON, Canada
- MR Author ID: 246969
- 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
- MR Author ID: 126270
- Email: umolter@dm.uba.ar
- 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
- © Copyright 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 138 (2010), 3965-3974
- MSC (2010): Primary 28A78, 28A80
- DOI: https://doi.org/10.1090/S0002-9939-2010-10396-9
- MathSciNet review: 2679618