Geodesic
A variant of a metric for unbounded convex sets
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 5 (2013) no. 1, pp. 40-49

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Convex analysis methods are used for the construction of distance function between closed (un­bounded in common case) sets of Euclidean space. It is shown that the distance satisfies all properties of metric. It is proved that this distance is invariant under motion of the sets in space. This metric space is proved to be complete.
Mots-clés : Hausdorff distance
Keywords: metric, convex set, recessive cone. 
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     title = {A variant of a metric for unbounded convex sets},
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P. D. Lebedev; V. N. Ushakov. A variant of a metric for unbounded convex sets. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 5 (2013) no. 1, pp. 40-49. http://geodesic.mathdoc.fr/item/VYURM_2013_5_1_a6/