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On the Hausdorff dimension of ultrametric subsets in ℝⁿ

James R. Lee; Manor Mendel; Mohammad Moharrami — 2012

Fundamenta Mathematicae

For every ε > 0, any subset of ℝⁿ with Hausdorff dimension larger than (1-ε)n must have ultrametric distortion larger than 1/(4ε).

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