Abstract
Weak convergence of convolution products of non-identical probability measures on topological semigroups is investigated. Firstly, the dependence relationship between the semigroupN 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.
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