摘要
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.
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.
基金
Project supported by the National Natural Science Foundation of China and the Natural Science Foundation of Shandong Province,China
