A Simple Sampling Method for Metric Measure Spaces

Details A Simple Sampling Method for Metric Measure Spaces A Simple Sampling Method for Metric Measure Spaces

2011-03-20

arxiv.org/abs/1103.3843v1

Computer Science

Information Theory

34 pages

Scientific paper

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.

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