Probabilistic convergence transformation groups

Journal Article
jaeger, T M G Ahsanullah and Gunther . 2018
Publication Work Type: 
Original Research
Magazine \ Newspaper: 
Mathematica Slovaca
Issue Number: 
6
Volume Number: 
68
Pages: 
1447-1467
Publication 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.