IJPAM: Volume 105, No. 2 (2015)

A CONTRIBUTION TO THE STUDY OF
THE PROBABILISTIC HAUSDORFF METRIC

Abderrahim Mbarki$^1$, Rachid Naciri$^2$
$^1$national School of Applied Sciences
P.O. Box 669, Oujda University
Matsi Laboratory, MOROCCO
$^2$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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DOI: 10.12732/ijpam.v105i2.4 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 105
Issue: 2
Pages: 163 - 172


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