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

Abstract

For $d\geq 2$, we construct a doubling measure $ν$ on $\R^d$ and a rectifiable curve $Γ$ such that $ν(Γ)>0$.

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