A doubling measure on ${\mathbb{R}}^d$ can charge a rectifiable curve

Abstract

For $d\ge 2$, we construct a doubling measure $\nu$ on ${\mathbb{R}}^d$ and a rectifiable curve $\Gamma$ such that $\nu (\Gamma )>0$.

8 pages. 1 figure. V2: Minor changes made after ref. report. To appear in Proc. of the AMS