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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.
Content available remote Autonomous differential inclusion sharing the families of trajectories
We give a sufficient condition for equality of sets of trajectories of two differential inclusions with right-hand sides Borel measurable with respect to the state variable, not necessarily bounded and possibly containing the origin.
Content available remote A note on measures on time scales
A connection between the measures used on time scales and usual Lebesgue measure is established and applied to simple justifications of some recently published results on Vitali covering theorem and (delta)-differentiability of monotone functions defined on time scales.
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