On the Hausdorff dimension of ultrametric subsets in $\mathbb R^n$

Tom 218 / 2012

James R. Lee, Manor Mendel, Mohammad Moharrami Fundamenta Mathematicae 218 (2012), 285-290 MSC: 30L05, 37F35. DOI: 10.4064/fm218-3-5

Streszczenie

For every $\varepsilon>0$, any subset of $\mathbb{R}^n$ with Hausdorff dimension larger than $(1-\varepsilon)n$ must have ultrametric distortion larger than $1/(4\varepsilon)$.

Autorzy

  • James R. LeeDepartment of Computer Science
    and Engineering
    Box 352350
    University of Washington
    Seattle, WA 98195-2350, U.S.A.
    e-mail
  • Manor MendelMathematics and
    Computer Science Department
    The Open University of Israel
    1 University Rd., P.O. Box 808
    Raanana 43107, Israel
    e-mail
  • Mohammad MoharramiDepartment of Computer Science and Engineering
    Box 352350
    University of Washington
    Seattle, WA 98195-2350, U.S.A.
    e-mail

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