Limits of commutative triangular systems on locally compact groups

On a locally compact group G, if , for some probability measuresv _n and μ onG, then a sufficient condition is obtained for the set to be relatively compact; this in turn implies the embeddability of a shift of μ. The condition turns out to be also necessary when G is totally disconnected. In particular, it is shown that ifG is a discrete linear group over R then a shift of the limit μ is embeddable. It is also shown that any infinitesimally divisible measure on a connected nilpotent real algebraic group is embeddable.