On Plis Metric on the Space of Strictly Convex Compacta

We consider a certain metric on the space of all convex compacta in Rn, introduced by A. Plis ["Uniqueness of optimal trajectories for non-linear control problems, Ann. Polon. Math. 29 (1975), 397-401]. The set of strictly convex compacta is a complete metric subspace of the metric space of convex compacta with respect to this metric. We present some applications of this metric to the problems of set-valued analysis, in particular we estimate the distance between two compact sets with respect to this metric and to the Hausdorff metric.