Strong uniform convergence of composition sequences of probability measures on locally compact topological semigroups

Weak convergence of convolution products of non-identical probability measures on topological semigroups is investigated Firstly, the dependence relationship between the semigroup N of measures and suppN is studied; secondly, a necessary and sufficient condition that insures the strong uniform composition convergence of sequence |μn| is presented; thirdly, a more extensive class of semigroups is found, on which |μn| must be of strong uniform composition convergence, if it is of composition convergence.