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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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