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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| Format: | Article |
| Language: | English |
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Wiley
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/S016117129200022X |
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| _version_ | 1832565512151760896 |
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| author | N. A. Tserpes |
| author_facet | N. A. Tserpes |
| author_sort | N. A. Tserpes |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-65ed6fdb4f964e8f968bb6499a89ea8f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1992-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-65ed6fdb4f964e8f968bb6499a89ea8f2025-02-03T01:07:27ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251992-01-0115119519810.1155/S016117129200022XA note on conservative measures on semigroupsN. A. Tserpes0Department of Mathematics, University of Patra, Patra, GreeceConsider (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.http://dx.doi.org/10.1155/S016117129200022Xtopological metric semigroupsleft groupsconservative translations of the semigroupBorel measurer*-invariant measures. |
| spellingShingle | N. A. Tserpes A note on conservative measures on semigroups International Journal of Mathematics and Mathematical Sciences topological metric semigroups left groups conservative translations of the semigroup Borel measure r*-invariant measures. |
| title | A note on conservative measures on semigroups |
| title_full | A note on conservative measures on semigroups |
| title_fullStr | A note on conservative measures on semigroups |
| title_full_unstemmed | A note on conservative measures on semigroups |
| title_short | A note on conservative measures on semigroups |
| title_sort | note on conservative measures on semigroups |
| topic | topological metric semigroups left groups conservative translations of the semigroup Borel measure r*-invariant measures. |
| url | http://dx.doi.org/10.1155/S016117129200022X |
| work_keys_str_mv | AT natserpes anoteonconservativemeasuresonsemigroups AT natserpes noteonconservativemeasuresonsemigroups |