Abstract

In this paper, we give the notion of locally convex probabilistic seminormed spaces and discuss some property of locally convex probabilistic seminormed spaces.

Highlights

  • Convex probabilistic normed spaces are an interesting topic

  • The concept of locally convex probabilistic normed spaces has been introduced following the definition of Šerstnev through the intersection of two concepts of locally convex spaces and probabilistic normed spaces

  • We prove some examples of locally convex probabilistic Šerstnev semi-normed spaces (Theorem . and Theorem . )

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Summary

Introduction

Convex probabilistic normed spaces are an interesting topic. some papers [ – ] discussed the subject, and we enjoy the topic too. Let V be a vector space, and υ be a Š-probabilistic seminorm with τ and υ satisfying the following condition: (ŠPSN ) For any p, q ∈ V, t , t > , if υp(t ) > – λ and υq(t ) > – λ, υp+q(t + t ) > – λ.

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