Finite and countable infinite products of Probabilistic Normed Spaces

摘要

In this work we first give for PN spaces results parallel to those obtainedby Egbert for the product of PM spaces, and generalize results by Alsina andSchweizer in order to study non-trivial products and the product of $m$--transforms of several PN spaces. In addition we present a detailed study of $\alpha$--simple product PN spacesand, finally, the product topologies in PN spaces which are products ofcountable families of PN spaces.