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.
@article{bwmeta1.element.doi-10_2478_agms-2012-0003,
author = {Guy David and Marie Snipes},
title = {A Non-Probabilistic Proof of the Assouad Embedding Theorem with Bounds on the Dimension},
journal = {Analysis and Geometry in Metric Spaces},
volume = {1},
year = {2013},
pages = {36-41},
zbl = {1261.53039},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_agms-2012-0003}
}
Guy David; Marie Snipes. A Non-Probabilistic Proof of the Assouad Embedding Theorem with Bounds on the Dimension. Analysis and Geometry in Metric Spaces, Tome 1 (2013) pp. 36-41. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_agms-2012-0003/
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A. Naor and O. Neiman, Assouad’s theorem with dimension independent of the snowflaking, Revista Matemática Iberoamericana 28 (4), 1–21, 2012 [WoS] | Zbl 1260.46016