An Extension of a result of Csiszar

P. B. Cerrito

International Journal of Mathematics and Mathematical Sciences, 1986, vol. 9, 1-9

Abstract:

We extend the results of Csiszar (Z. Wahr. 5(1966) 279-295) to a topological semigroup S . Let μ be a measure defined on S . We consider the value of α = sup K compact lim n → ∞ sup x ∈ S μ n ( K x − 1 ) . First. we show that the value of α is either zero or one. If α = 1 , we show that there exists a sequence of elements { a n } In S such that μ n ∗ δ a n converges vaguely to a probability measure where δ denotes point mass. In particular, we apply the results to inverse and matrix semigroups.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:135913

DOI: 10.1155/S0161171286000042

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