Calculus of Variations and Geometric Measure Theory

G. Buttazzo - B. Schweizer

$\Gamma$ convergence of Hausdorff measures

created on 31 Jul 2002
modified on 25 Oct 2002


Submitted Paper

Inserted: 31 jul 2002
Last Updated: 25 oct 2002

Year: 2002


We study the dependence of the Hausdorff measure $\H1_d$ on the distance $d$. We show that the uniform convergence of $d_j$ to $d$ is equivalent to the $\Gamma$ convergence of $\H1_{d_j}$ to $\H1_d$ with respect to the Hausdorff convergence on compact connected subsets. We also consider the case when distances are replaced by semi-distances.

Keywords: $\Gamma$ convergence, Hausdorff measures, Golab theorem