Countable products of probabilistic normed spaces (original) (raw)

NORMABILITY OF PROBABILISTIC NORMED SPACES

Relying on Kolmogorov's classical characterization of normable Topological Vector spaces, we study the normability of those Probabilistic Normed Spaces that are also Topological Vector spaces and provide a characterization of normableŠerstnev spaces. We also study the normability of other two classes of Probabilistic Normed Spaces.

A note on the probabilistic N-Banach spaces

arXiv (Cornell University), 2016

In this paper, we define probabilistic n-Banach spaces along with some concepts in this field and study convergence in these spaces by some lemmas and theorem.

On α-Šerstnev probabilistic normed spaces

Journal of Inequalities and Applications, 2011

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.

A Mazur–Ulam theorem for probabilistic normed spaces

Aequationes mathematicae, 2009

A classical theorem of S. Mazur and S. Ulam asserts that any surjective isometry between two normed spaces is an affine mapping. D. Mushtari proved in 1968 the same result in the case of random normed spaces in the sense of A. Sherstnev. The aim of the present paper is to show that the result holds also for the probabilistic normed spaces as defined by C. Alsina, B. Schweizer and A. Sklar, Aequationes Math. 46 (1993), 91-98.

Probabilistic n-normed spaces, D-n-compact sets and D-n-bounded sets

In this paper, first we define and study the probabilistic n-normed spaces and D-n-compactness, also we prove some theorems and inequalities. In the next section we define D-n-boundedness and prove some results in relation between D-n-compact and D-nbounded sets in these spaces.

An answer to one question about probabilistic metric spaces

A probabilistic metric space is a generalization of metric space /briefly a PM space/, in which the "distance" between any two points is a probability distribution function rather than a definite number. While a probabilistic metric space generated by a (strongly) mixing transformation is essentially equilateral, spaces generated by arbitrary measure-preserving transformations are more varied.

Ideal convergent sequences of functions in probabilistic normed spaces

The journal of mathematics and computer science, 2021

In the present article, we have defined the notion of I-pointwise convergence and I-uniform convergence of sequence of functions defined on a probabilistic normed space with respect to the probabilistic norm ν. Further we have given the Cauchy criteria for I-pointwise and I-uniform convergence in PNS. Also, we have proved certain results on continuity of functions with respect to ν in PNS.