On the normability of generalized Šerstnev PN spaces
Copyright policy )On the normability of generalized Šerstnev PN spaces
Probabilistic Normed spaces were introduced by \textit{A. N. Serstnev} [Docl. Akad. Nauk SSSR 149, 280--283 (1963; Zbl 0127.34902)] and redefined by \textit{C. Alsina, B. Schweizer} and \textit{A. Sklar} [Aequationes Math. 46, 91--98 (1993; Zbl 0792.46062)]. The authors adopt the definition of Alsina, Schweizer and Sklar for Probabilistic Normed spaces, called generalized Serstnev PN spaces. It is an open question whether a generalized Serstnev PN space is normable. In this paper some sufficient conditions for normability are given. The investigation is related to Kolmogorov's classical characterization of normability for \( T_1\) spaces [\textit{A. N. Kolmogorov}, Studia Math. 5, 29--33 (1934; JFM 60.1229.02)].
- Southwestern University of Finance and Economics China (People's Republic of)
- Chengdu University of Information Technology China (People's Republic of)
Probability theory on linear topological spaces, locally convex, Applied Mathematics, topologically bounded, Topologically bounded, Normability, Probabilistic metric spaces, Probabilistic methods in Banach space theory, normability, Locally convex, Analysis
Probability theory on linear topological spaces, locally convex, Applied Mathematics, topologically bounded, Topologically bounded, Normability, Probabilistic metric spaces, Probabilistic methods in Banach space theory, normability, Locally convex, Analysis
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