Abderrahim Mbarki, Rachid Naciri
national School of Applied Sciences
P.O. Box 669, Oujda University
Matsi Laboratory, MOROCCO
Matsi Laboratory
Oujda University
60000, Oujda, MOROCCO

Abstract. The purpose of the present paper is to study several important properties of the probabilistic Hausdorff metric. Indeed, we prove that the collection of nonempty compact subsets of a probabilistic metric space is complete with respect to the probabilistic Hausdorff metric if and only if the probabilistic metric space is complete . As a consequence, the relationship between completion of the probabilistic Hausdorff metric for a given PM space and probabilistic Hausdorff metric of its completion is examined. Finally, Deterministic counterpart of these results is deduced. Our work extend some results of [2] and [12].

Received: August 7, 2015

AMS Subject Classification: 54E70, 54A40, 54B20

Key Words and Phrases: probabilistic Hausdorff metric, complete, isometric

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