A note on the support of right invariant measures
A regular measure μ on a locally compact topological semigroup is called right invariant if μ(Kx)=μ(K) for every compact K and x in its support. It is shown that this condition implies a property reminiscent of the right cancellation law. This is used to generalize a theorem of A. Mukherjea and the...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
1992-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S016117129200053X |
| Summary: | A regular measure μ on a locally compact topological semigroup is called right invariant if μ(Kx)=μ(K) for every compact K and x in its support. It is shown that this condition implies a property reminiscent of the right cancellation law. This is used to generalize a theorem of A. Mukherjea and the author (with a new proof) to the effect that the support of an r*-invariant measure is a left group iff the measure is right invariant on its support. |
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| ISSN: | 0161-1712 1687-0425 |