The Demyanov metric in the family of convex, compact sets in finite dimensional spaces has been recently extended to the family of convex, bounded sets – not necessarily closed. In this note it is shown that these spaces are not complete and a model for the completion is proposed. A full answer is given in R2 and the situation in higher dimensions is discussed.
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We present in this paper measurability multifunctions in the family of all convex, bounded sets which need not be closed. The Demyanov metric is discussed.
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