Selfdecomposable Measures on Simply Connected Nilpotent Groups

The concepts of class L measures and selfdecomposable measures are generalised from vector spaces to simply connected nilpotent groups G. It has been shown that any full class L (probability) measure (mu) on G can be decomposed as (mu)= (mu)1 * ... * (mu) n, where each (mu)i is a selfdecomposable measure on a subgroup G i; (mu) itself is selfdecomposable under certain additional conditions-for example, when (mu) is symmetric. This generalizes a well known result on vector spaces. Some examples of class L measures on G are also constructed.