Journal of convex analysis, Tome 12 (2005) no. 1, pp. 239-253
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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/
@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},
year = {2005},
volume = {12},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JCA_2005_12_1_JCA_2005_12_1_a16/}
}
TY - JOUR
AU - G. Buttazzo
AU - B. Schweizer
TI - Γ Convergence of Hausdorff Measures
JO - Journal of convex analysis
PY - 2005
SP - 239
EP - 253
VL - 12
IS - 1
UR - http://geodesic.mathdoc.fr/item/JCA_2005_12_1_JCA_2005_12_1_a16/
ID - JCA_2005_12_1_JCA_2005_12_1_a16
ER -
%0 Journal Article
%A G. Buttazzo
%A B. Schweizer
%T Γ Convergence of Hausdorff Measures
%J Journal of convex analysis
%D 2005
%P 239-253
%V 12
%N 1
%U http://geodesic.mathdoc.fr/item/JCA_2005_12_1_JCA_2005_12_1_a16/
%F JCA_2005_12_1_JCA_2005_12_1_a16
\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.
