A Non-Probabilistic Proof of the Assouad Embedding Theorem with Bounds on the Dimension-Reference-Cited by-同舟云学术

A Non-Probabilistic Proof of the Assouad Embedding Theorem with Bounds on the Dimension

Published:2013-01-14 Issue: Volume:1 Page:36-41
ISSN:2299-3274
Container-title:Analysis and Geometry in Metric Spaces
language:
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Author:

David Guy,Snipes Marie

Abstract

Abstract We give a non-probabilistic proof of a theorem of Naor and Neiman that asserts that if (E, d) is a doubling metric space, there is an integer N > 0, depending only on the metric doubling constant, such that for each exponent α ∈ (1/2; 1), one can find a bilipschitz mapping F = (E; dα ) ⃗ ℝ RN.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Geometry and Topology,Analysis

Link

https://www.degruyter.com/view/j/agms.2012.1.issue/agms-2012-0003/agms-2012-0003.pdf

Reference3 articles.

1. s theorem with dimension independent of the snowflaking;Naor;Revista,2012

2. Lectures on Analysis on Metric Spaces Verlag;Heinonen,2001

3. lipschitziens dans;Assouad;Bull Soc Math,1983

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