Journal of Convex Analysis 12 (2005), No. 1, 239--253
Copyright 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.
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