Selfdecomposable measures on simply connected nilpotent groups

The concepts of class L measures and selfdecomposable measures are generali sed from vector splices to simply connected nilpotent groups G. it has been shown that any full class L (probability) measure mu on G can be decompose d as mu = mu(1 *) . . . (*) mu(n,) where each mu(i) is a selfdecomposable m easure on a subgroup G(i); mu itself is selfdecomposable under certain addi tional conditions for example. when ii is symmetric, This generalizes a wel l known result on vector spaces. Some examples of class L measures on G are also constructed.