Abstract
Abstract : The purpose of this paper is to consider some measures of noncompactness and their application to fixed point theorems for random operators. In a subsequent paper we will consider applications of these results to random operator equations. This paper is not the first to consider measures of noncompactness in probabilistic analysis. We refer to the book of Constantin and Istratescu for results on measures of noncompactness and probabilistic metric spaces. Section 2 gives some basic definitions of measures of noncompactness, and lists their properties. Section 3 is devoted to applications of measures of noncompactness to fixed point theorems for random operators. Keywords include: Operators (Mathematics), Probability, Noncompactness.
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