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

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

2009-06-13

arxiv.org/abs/0906.2484v2

Mathematics

Metric Geometry

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

Scientific paper

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

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