Applications of outer measures to separation properties of lattices and regular or σ-smooth measures
Associated with a 0−1 measure μ∈I(ℒ) where ℒ is a lattice of subsets of X are outer measures μ′ and μ˜; associated with a σ-smooth 0−1 measure μ∈Iσ(ℒ) is an outer measure μ″ or with μ∈Iσ(ℒ′), ℒ′ being the complementary lattice, another outer measure μ˜˜. These outer measures and their associated mea...
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| Format: | Article |
| Language: | English |
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Wiley
1996-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S016117129600035X |
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| _version_ | 1841524525140803584 |
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| author | Pao-Sheng Hsu |
| author_facet | Pao-Sheng Hsu |
| author_sort | Pao-Sheng Hsu |
| collection | DOAJ |
| description | Associated with a 0−1 measure μ∈I(ℒ) where ℒ is a lattice of subsets of X are outer measures μ′ and μ˜; associated with a σ-smooth 0−1 measure μ∈Iσ(ℒ) is an outer measure μ″ or with μ∈Iσ(ℒ′), ℒ′ being the complementary lattice, another outer measure μ˜˜. These outer measures and their associated measurable sets are used to establish separation properties on ℒ and regularity and σ-smoothness of μ. Separation properties between two lattices ℒ1 and ℒ2, ℒ1⫅ℒ2, are similarly investigated. Notions of strongly σ-smooth and slightly regular measures are also used. |
| format | Article |
| id | doaj-art-3355ae3d072e4b0d9824b78039cc8d8a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1996-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3355ae3d072e4b0d9824b78039cc8d8a2025-02-03T05:52:54ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251996-01-0119225326210.1155/S016117129600035XApplications of outer measures to separation properties of lattices and regular or σ-smooth measuresPao-Sheng Hsu0University of Maine, Orono 04669-5752, Maine, USAAssociated with a 0−1 measure μ∈I(ℒ) where ℒ is a lattice of subsets of X are outer measures μ′ and μ˜; associated with a σ-smooth 0−1 measure μ∈Iσ(ℒ) is an outer measure μ″ or with μ∈Iσ(ℒ′), ℒ′ being the complementary lattice, another outer measure μ˜˜. These outer measures and their associated measurable sets are used to establish separation properties on ℒ and regularity and σ-smoothness of μ. Separation properties between two lattices ℒ1 and ℒ2, ℒ1⫅ℒ2, are similarly investigated. Notions of strongly σ-smooth and slightly regular measures are also used.http://dx.doi.org/10.1155/S016117129600035Xnormal latticesemi-separatesseparatescomplement generatedcountably paracompactcountably compact. regularσ-smoothstrongly σ-smoothslightly regular measures; μ*-measurable sets. |
| spellingShingle | Pao-Sheng Hsu Applications of outer measures to separation properties of lattices and regular or σ-smooth measures International Journal of Mathematics and Mathematical Sciences normal lattice semi-separates separates complement generated countably paracompact countably compact. regular σ-smooth strongly σ-smooth slightly regular measures; μ*-measurable sets. |
| title | Applications of outer measures to separation properties of lattices and regular or σ-smooth measures |
| title_full | Applications of outer measures to separation properties of lattices and regular or σ-smooth measures |
| title_fullStr | Applications of outer measures to separation properties of lattices and regular or σ-smooth measures |
| title_full_unstemmed | Applications of outer measures to separation properties of lattices and regular or σ-smooth measures |
| title_short | Applications of outer measures to separation properties of lattices and regular or σ-smooth measures |
| title_sort | applications of outer measures to separation properties of lattices and regular or σ smooth measures |
| topic | normal lattice semi-separates separates complement generated countably paracompact countably compact. regular σ-smooth strongly σ-smooth slightly regular measures; μ*-measurable sets. |
| url | http://dx.doi.org/10.1155/S016117129600035X |
| work_keys_str_mv | AT paoshenghsu applicationsofoutermeasurestoseparationpropertiesoflatticesandregularorssmoothmeasures |