Geodesic
Γ Convergence of Hausdorff Measures
Journal of convex analysis, Tome 12 (2005) no. 1, pp. 239-253.

Voir la notice de l'article provenant de la source Heldermann Verlag

\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. 
@article{JCA_2005_12_1_JCA_2005_12_1_a16,
     author = {G. Buttazzo and B. Schweizer},
     title = {\ensuremath{\Gamma} {Convergence} of {Hausdorff} {Measures}},
     journal = {Journal of convex analysis},
     pages = {239--253},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2005},
     url = {http://geodesic.mathdoc.fr/item/JCA_2005_12_1_JCA_2005_12_1_a16/}
}
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G. Buttazzo; B. Schweizer. Γ Convergence of Hausdorff Measures. Journal of convex analysis, Tome 12 (2005) no. 1, pp. 239-253. http://geodesic.mathdoc.fr/item/JCA_2005_12_1_JCA_2005_12_1_a16/