It is shown that for every K > 0 and ε ∈ (0, 1/2) there exist N = N(K) ∈ N and D = D(K, ε) ∈ (1,∞) with the following properties. For every metric space (X, d) with doubling constant at most K, themetric space (X, d1-ε) admits a bi-Lipschitz embedding into RN with distortion at most D. The classical Assouad embedding theorem makes the same assertion, but with N →∞ as ε → 0.
|Original language||English (US)|
|Number of pages||20|
|Journal||Revista Matematica Iberoamericana|
|State||Published - 2012|
All Science Journal Classification (ASJC) codes
- Assouad's theorem
- Doubling metric spaces