An Extension of a result of Csiszar
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 {a...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1986-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171286000042 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |