Invariant and semi-invariant probabilistic normed spaces

M.B. Ghaemi, B. Lafuerza-Guillén and S. Saiedinezhad

Chaos, Solitons & Fractals, 2009, vol. 42, issue 1, 256-264

Abstract: Probabilistic metric spaces were introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of probabilistic normed space based on the definition of Menger [1]. We introduce the concept of semi-invariance among the PN spaces. In this paper we will find a sufficient condition for some PN spaces to be semi-invariant. We will show that PN spaces are normal spaces. Urysohn’s lemma, and Tietze extension theorem for them are proved.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:42:y:2009:i:1:p:256-264

DOI: 10.1016/j.chaos.2008.11.017

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