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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1995-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171295000937 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |