Lattice separation, coseparation and regular measures
Let X be an arbitrary non-empty set, and let ℒ, ℒ1, ℒ2 be lattices of subsets of X containing ϕ and X. 𝒜(ℒ) designates the algebra generated by ℒ and M(ℒ), these finite, non-trivial, non-negative finitely additive measures on 𝒜(ℒ). I(ℒ) denotes those elements of M(ℒ) which assume only the values z...
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
1996-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S016117129600107X |
| Summary: | Let X be an arbitrary non-empty set, and let ℒ, ℒ1, ℒ2
be lattices of subsets of X
containing
ϕ and X. 𝒜(ℒ) designates the algebra generated by ℒ and M(ℒ), these finite, non-trivial,
non-negative finitely additive measures on 𝒜(ℒ). I(ℒ) denotes those elements of M(ℒ) which assume
only the values zero and one. In terms of a μ∈M(ℒ) or I(ℒ), various outer measures are introduced.
Their properties are investigated. The interplay of
measurability, smoothness of μ, regularity of μ and
lattice topological properties on these outer measures is also investigated. |
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| ISSN: | 0161-1712 1687-0425 |