Probabilistic convergence transformation groups

Abstract

Abstract We introduce a notion of a probabilistic convergence transformation group, and present various natural examples including quotient probabilistic convergence transformation group. In doing so, we construct a probabilistic convergence structure on the group of homeomorphisms and look into a probabilistic convergence group that arises from probabilistic uniform convergence structure on function spaces. Given a probabilistic convergence space, and an arbitrary group, we construct a probabilistic convergence transformation group. Introducing a notion of a probabilistic metric convergence transformation group on a probabilistic metric space, we obtain in a natural way a probabilistic convergence transformation group.