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Journal of Convex Analysis 06 (1999), No. 2, 367--376
Copyright Heldermann Verlag 1999

Invariants of Pairs of Compact Convex Sets

Diethard Pallaschke
Inst. f. Statistik und Mathematische Wirtschaftstheorie, Universität Karlsruhe, Kaiserstr. 12, 76128 Karlsruhe, Germany

Ryszard Urbanski
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznan, Poland

In a recent paper P. Diamond, P. Kloeden, A. Rubinov and A. Vladimirov [Set-Valued Analysis (2000)] investigated comperative properties of three different metrics in the space of pairs of compact convex sets. These metrics describe invariant properties  of the Radström-Hörmander lattice i.e. the space of equivalence classes of pairs of nonempty compact convex sets. In this paper we consider invariants of a class of equivalent pairs of nonempty compact convex sets. We show that the affine dimension of the minimal representant of an equivalence class is invariant and that each equivalence class has invariant convexificators.

Keywords: Pairs of convex sets, sublinear function, quasidifferential calculus.

MSC: 52A07; 26A27, 90C30

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