On the definition of a probabilistic normed group

Abstract

Probabilistic normed spaces were introduced by Šerstnev and have been redefined by Alsina, Schweizer, and Sklar. In this paper, we introduce new spaces that are extension of the probabilistic normed spaces. Moreover, we obtain some conditions under which such spaces are topological groups. Also we define τ-products and countable products of these spaces.

Keywords:

• probabilistic normed group
• probabilistic normed space
• topological group
• τ-products
• countable products

AMS Subject Classications:

• Primary 54E70
• Secondary 46S70