Convolution Sequences of Measures on the Semigroup of Stochastic Matrices

摘要

Results on the asymptotic behavior of a convolution sequence upsilon n = 1,2,... of a regular probability measure upsilon on a compact topological semigroup S are given. If there is a limiting measure eta, it is concentrated on the kernel of the semigroup. The results are interpreted in the case of a semigroup S of stochastic matrices. The extent to which corresponding results hold or are open in the case of a noncompact S is commented on.