Geodesic
On the Hausdorff dimension of ultrametric subsets in $\mathbb R^n$
James R. Lee1 ; Manor Mendel2 ; Mohammad Moharrami1
1 Department of Computer Science and Engineering Box 352350 University of Washington Seattle, WA 98195-2350, U.S.A.
2 Mathematics and Computer Science Department The Open University of Israel 1 University Rd., P.O. Box 808 Raanana 43107, Israel
Fundamenta Mathematicae, Tome 218 (2012) no. 3, pp. 285-290.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

For every $\varepsilon>0$, any subset of $\mathbb{R}^n$ with Hausdorff dimension larger than $(1-\varepsilon)n$ must have ultrametric distortion larger than $1/(4\varepsilon)$.
DOI : 10.4064/fm218-3-5
Keywords: every varepsilon subset mathbb hausdorff dimension larger varepsilon have ultrametric distortion larger varepsilon

James R. Lee 1 ; Manor Mendel 2 ; Mohammad Moharrami 1

1 Department of Computer Science and Engineering Box 352350 University of Washington Seattle, WA 98195-2350, U.S.A.
2 Mathematics and Computer Science Department The Open University of Israel 1 University Rd., P.O. Box 808 Raanana 43107, Israel 
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James R. Lee; Manor Mendel; Mohammad Moharrami. On the Hausdorff dimension of ultrametric subsets in $\mathbb R^n$. Fundamenta Mathematicae, Tome 218 (2012) no. 3, pp. 285-290. doi : 10.4064/fm218-3-5. http://geodesic.mathdoc.fr/articles/10.4064/fm218-3-5/

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