Outer measures associated with lattice measures and their application
Consider a set X and a lattice ℒ of subsets of X such that ϕ, X∈ℒ. M(ℒ) denotes those bounded finitely additive measures on A(ℒ) which are studied, and I(ℒ) denotes those elements of M(ℒ) which are 0−1 valued. Associated with a μ∈M(ℒ) or a μ∈Mσ(ℒ) (the elements of M(ℒ) which are σ-smooth on ℒ) are o...
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| Format: | Article |
| Language: | English |
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Wiley
1995-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171295000937 |
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| _version_ | 1832558149463179264 |
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| author | Charles Traina |
| author_facet | Charles Traina |
| author_sort | Charles Traina |
| collection | DOAJ |
| description | Consider a set X and a lattice ℒ of subsets of X such that ϕ, X∈ℒ. M(ℒ) denotes
those bounded finitely additive measures on A(ℒ) which are studied, and I(ℒ) denotes those elements
of M(ℒ) which are 0−1 valued. Associated with a μ∈M(ℒ) or a μ∈Mσ(ℒ) (the elements of M(ℒ)
which are σ-smooth on ℒ) are outer measures μ′ and μ″. In terms of these outer measures various
regularity properties of μ can be introduced, and the interplay between regularity, smoothness, and
measurability is investigated for both the 0−1 valued case and the more general case. Certain results
for the special case carry over readily to the more general case or with at most a regularity assumption
on μ′ or μ″, while others do not. Also, in the special case of 0−1 valued measures more refined
notions of regularity can be introduced which have no immediate analogues in the general case. |
| format | Article |
| id | doaj-art-04aeac11d8034e51af08f8edcc4ac663 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1995-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-04aeac11d8034e51af08f8edcc4ac6632025-02-03T01:32:59ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251995-01-0118472573410.1155/S0161171295000937Outer measures associated with lattice measures and their applicationCharles Traina0St. John's University, Department of Mathematics & Computer Science, Jamaica 11439, NY, USAConsider a set X and a lattice ℒ of subsets of X such that ϕ, X∈ℒ. M(ℒ) denotes those bounded finitely additive measures on A(ℒ) which are studied, and I(ℒ) denotes those elements of M(ℒ) which are 0−1 valued. Associated with a μ∈M(ℒ) or a μ∈Mσ(ℒ) (the elements of M(ℒ) which are σ-smooth on ℒ) are outer measures μ′ and μ″. In terms of these outer measures various regularity properties of μ can be introduced, and the interplay between regularity, smoothness, and measurability is investigated for both the 0−1 valued case and the more general case. Certain results for the special case carry over readily to the more general case or with at most a regularity assumption on μ′ or μ″, while others do not. Also, in the special case of 0−1 valued measures more refined notions of regularity can be introduced which have no immediate analogues in the general case.http://dx.doi.org/10.1155/S0161171295000937normal latticelattice regular measuresassociated outer measures. |
| spellingShingle | Charles Traina Outer measures associated with lattice measures and their application International Journal of Mathematics and Mathematical Sciences normal lattice lattice regular measures associated outer measures. |
| title | Outer measures associated with lattice measures and their application |
| title_full | Outer measures associated with lattice measures and their application |
| title_fullStr | Outer measures associated with lattice measures and their application |
| title_full_unstemmed | Outer measures associated with lattice measures and their application |
| title_short | Outer measures associated with lattice measures and their application |
| title_sort | outer measures associated with lattice measures and their application |
| topic | normal lattice lattice regular measures associated outer measures. |
| url | http://dx.doi.org/10.1155/S0161171295000937 |
| work_keys_str_mv | AT charlestraina outermeasuresassociatedwithlatticemeasuresandtheirapplication |