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

• DOI: 10.48550/arxiv.0906.2484
• Publication Date: 2009-01-01
• Authors: John B. Garnett; Rowan Killip; Raanan Schul
• Keywords: Mathematics - Metric Geometry; Mathematics - Classical Analysis and ODEs; Classical Analysis and ODEs (math.CA); FOS: Mathematics; Anàlisi harmònica; Metric Geometry (math.MG); 517 - Anàlisi; 0101 mathematics; 01 natural sciences

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