A note on conservative measures on semigroups
Consider (S,B,μ) the measure space where S is a topological metric semigroup and μ a countably additive bounded Borel measure. Call μ conservative if all right translations tx:s→sx, x∈S (which are assumed closed mappings) are conservative with respect (S,B,μ) in the ergodic theory sense. It is shown...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1992-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S016117129200022X |
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| Summary: | Consider (S,B,μ) the measure space where S is a topological metric semigroup and μ a countably additive bounded Borel measure. Call μ conservative if all right translations tx:s→sx, x∈S (which are assumed closed mappings) are conservative with respect (S,B,μ) in the ergodic theory sense. It is shown that the semigroup generated by the support of μ is a left group. An extension of this result is obtained for σ-finite μ. |
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| ISSN: | 0161-1712 1687-0425 |