ON SZASZ’S COMPACTNESS THEOREM AND APPLICATIONS TO
GEOMETRIC STABILITY ON GROUPS
Abstract: Within the rapidly developing theory of random limit theory for real-valued random
variables the concepts of geometric convolution and geometric stability play a fundamental
role. In several recent investigations it was pointed out that there is a one-to-one
correspondence between “classical” limit theorems and stability concepts and their geometric
counterparts (cf. [2], [3], [5], [11], [14]-[16]).
We are going to prove analogous results for randomized products of random variables
taking values in a simply connected nilpotent Lie group 
This class of groups is natural in
this setup since classical stability concepts were generalized to nilpotent groups (cf. [6] and
[17]).
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -
