Remarks on μ″-measurbale sets: regularity, σ-smootheness, and measurability
Let X be an arbitrary nonempty set and ℒ a lattice of subsets of X such that ϕ,X∈ℒ. 𝒜(ℒ) is the algebra generated by ℒ and ℳ(ℒ) denotes those nonnegative, finite, finitely additive measures μ on 𝒜(ℒ). I(ℒ) denotes the subset of ℳ(ℒ) of nontrivial zero-one valued measures. Associated with μ∈I(ℒ) (or...
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| Format: | Article |
| Language: | English |
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Wiley
1999-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171299223915 |
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| _version_ | 1832562144827146240 |
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| author | Carman Vlad |
| author_facet | Carman Vlad |
| author_sort | Carman Vlad |
| collection | DOAJ |
| description | Let X be an arbitrary nonempty set and ℒ a lattice of subsets of X such that ϕ,X∈ℒ. 𝒜(ℒ) is the algebra generated by ℒ and ℳ(ℒ) denotes those nonnegative, finite, finitely additive measures μ on 𝒜(ℒ). I(ℒ) denotes the subset of ℳ(ℒ) of nontrivial zero-one valued measures. Associated with μ∈I(ℒ) (or Iσ(ℒ)) are the outer measures μ′ and μ″ considered in detail. In addition, measurability conditions and regularity conditions are investigated and specific characteristics are given for 𝒮μ″, the set of μ″-measurable sets. Notions of strongly σ-smooth and vaguely regular measures are also discussed. Relationships between regularity, σ-smoothness and measurability are investigated for zero-one valued measures and certain results are extended to the case of a pair of lattices ℒ1,ℒ2 where ℒ1⊂ℒ2. |
| format | Article |
| id | doaj-art-feaf4f968ce64aa48d49f5e571fd700e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1999-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-feaf4f968ce64aa48d49f5e571fd700e2025-02-03T01:23:23ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251999-01-0122239140010.1155/S0161171299223915Remarks on μ″-measurbale sets: regularity, σ-smootheness, and measurabilityCarman Vlad0Pace University, Pace Plaza, New York 10038, NY, USALet X be an arbitrary nonempty set and ℒ a lattice of subsets of X such that ϕ,X∈ℒ. 𝒜(ℒ) is the algebra generated by ℒ and ℳ(ℒ) denotes those nonnegative, finite, finitely additive measures μ on 𝒜(ℒ). I(ℒ) denotes the subset of ℳ(ℒ) of nontrivial zero-one valued measures. Associated with μ∈I(ℒ) (or Iσ(ℒ)) are the outer measures μ′ and μ″ considered in detail. In addition, measurability conditions and regularity conditions are investigated and specific characteristics are given for 𝒮μ″, the set of μ″-measurable sets. Notions of strongly σ-smooth and vaguely regular measures are also discussed. Relationships between regularity, σ-smoothness and measurability are investigated for zero-one valued measures and certain results are extended to the case of a pair of lattices ℒ1,ℒ2 where ℒ1⊂ℒ2.http://dx.doi.org/10.1155/S0161171299223915Outer measurecover regular outer measurestrongly σ-smooth and vaguely regular measures. |
| spellingShingle | Carman Vlad Remarks on μ″-measurbale sets: regularity, σ-smootheness, and measurability International Journal of Mathematics and Mathematical Sciences Outer measure cover regular outer measure strongly σ-smooth and vaguely regular measures. |
| title | Remarks on μ″-measurbale sets: regularity, σ-smootheness, and measurability |
| title_full | Remarks on μ″-measurbale sets: regularity, σ-smootheness, and measurability |
| title_fullStr | Remarks on μ″-measurbale sets: regularity, σ-smootheness, and measurability |
| title_full_unstemmed | Remarks on μ″-measurbale sets: regularity, σ-smootheness, and measurability |
| title_short | Remarks on μ″-measurbale sets: regularity, σ-smootheness, and measurability |
| title_sort | remarks on μ measurbale sets regularity σ smootheness and measurability |
| topic | Outer measure cover regular outer measure strongly σ-smooth and vaguely regular measures. |
| url | http://dx.doi.org/10.1155/S0161171299223915 |
| work_keys_str_mv | AT carmanvlad remarksonmmeasurbalesetsregularityssmoothenessandmeasurability |