A Non-Probabilistic Proof of the Assouad Embedding Theorem with Bounds on the Dimension
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.
Snipes, Marie and David, Guy, "A Non-Probabilistic Proof of the Assouad Embedding Theorem with Bounds on the Dimension" (2013). Analysis and Geometry in Metric Spaces 1. Faculty Publications. Paper 56.
Analysis and Geometry in Metric Spaces