On locally convex probabilistic normed spaces

Jie Chi,Changli Yan,Binshan Ju,Minxian Zhang

doi:10.1186/s13660-016-1263-1

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 . )

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.

Results

Conclusion