A Simple Sampling Method for Metric Measure Spaces
  We introduce a new, simple metric method of sampling metric measure spaces, based on a well-known "snowflakeing operator" and we show that, as a consequence of a classical result of Assouad, the sampling of doubling metric spaces is bilipschitz equivalent to that of subsets of some $\mathbb{R}^N$. Moreover, we compare this new method with two other approaches, in particular to one that represents a direct application of our triangulation method of metric measure spaces satisfying a generalized Ricci curvature condition. 
Emil Saucan
cs.IT math.IT math.MG