International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 1, Pages 29-37
doi:10.1155/S0161171286000042
An Extension of a result of Csiszar
Department of Mathematics, University of South Florida, Tampa 33620, Florida, USA
Received 22 July 1985
Copyright © 1986 P. B. Cerrito. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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=supKcompactlimn→∞supx∈Sμn(Kx−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 {an} In S such that μn∗δan converges vaguely to a probability measure where δ denotes point mass. In particular, we apply the results to inverse and matrix semigroups.