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A Non-Probabilistic Proof of the Assouad Embedding Theorem with Bounds on the Dimension
2013
Analysis and Geometry in Metric Spaces
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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.
doi:10.2478/agms-2012-0003
fatcat:7s3pfel6trfbpf7jmqvfuw5pyu