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A variant of a metric for unbounded convex sets. (Russian. English summary) Zbl 1331.49065

Summary: 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.

MSC:

49Q20 Variational problems in a geometric measure-theoretic setting
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
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