A dual characterization of length spaces with application to Dirichlet metric spaces
Volume 198 / 2010
Studia Mathematica 198 (2010), 221-233
MSC: Primary 30Lxx; Secondary 31C25.
DOI: 10.4064/sm198-3-2
Abstract
We show that under minimal assumptions, the intrinsic metric induced by a strongly local Dirichlet form induces a length space. The main input is a dual characterization of length spaces in terms of the property that the 1-Lipschitz functions form a sheaf.
