Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 12 (2005), No. 1, 239--253Copyright Heldermann Verlag 2005 Γ Convergence of Hausdorff Measures Giuseppe Buttazzo Dip. di Matematica, Università di Pisa, Via Buonarroti 2, 56127 Pisa, Italy buttazzo@dm.unipi.it Benjamin Schweizer Inst. Angewandte Mathematik, Universität Heidelberg, INF 294, 69120 Heidelberg, Germany schweizer@iwr.uni-heidelberg.de [Abstract-pdf] \def\H1{\mathcal{H}^1} 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. [ Fulltext-pdf  (446  KB)] for subscribers only.