On infinite divisibility and embedding of probability measures on a locally compact Abelian group

Abstract

In the present note the authors supplement significant properties of infinitely divisible and embeddable probability measures on a locally compact Abelian group G. There are at least two versions of infinite divisibility appearing in the literature which deserve special attention, and the problem of embedding those measures leads directly to the study of continuous convolution semigroups on G. It is evident from the classical setup of G = R for d> 1 that in this context Gaussian semigroups and measures play a favorite role.