D-bounded sets in probabilistic normed spaces and in their products

Abstract

A sufficient, but not necessary, condition is given for the family of D-bounded subsets in a Probabilistic Normed space(briefly PN space)to be a linear space when it is endowed with suitably defined operations of addition and multiplication by a scalar. In Section 3, tau-products of PN spaces are introduced and a sufficient condition is given for D-boundedness in tau-products.