The least doubling constant of a metric measure space

Abstract

We study the least doubling constant $C_{(X,d)}$, among all doubling measures $\mu$ supported on a metric space $(X,d)$. In particular, we prove that for every metric space with more than one point, $C_{(X,d)}\ge 2$. We also describe some further properties of $C_{(X,d)}$ and compute its value for several important examples.

16 pages. Theorem 3.1 has been included improving previous estimates for general metric spaces, and therefore some partial results from the older version have been removed