Probabilistic normed spaces have been redefined by Alsina, Schweizer, and Sklar. We give a detailed analysis of various boundedness notions for linear operators between such spaces and we study the relationship among them and also with the notion of continuity.
In this article, the condition a-Š is defined for a ]0, 1[∪]1, +∞[and several classes of a-Šerstnev PN spaces, the relationship between a-simple PN spaces and a-Šerstnev PN spaces and a study of PN spaces of linear operators which are a-Šerstnev PN spaces are given.
We prove that the probabilistic norms of suitable Probabilistic Normed spaces induce convergence in probability, LI' convergence and almost sure convergence. o 2003 Elsevier Science (USA). All rights reserved.
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