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 on G can be decomposed as = ₁* ... * _n, where each _i is a selfdecomposable measure on a subgroup G _i; itself is selfdecomposable under certain additional conditions—for example, when is symmetric. This generalizes a well known result on vector spaces. Some examples of class L measures on G are also constructed.