Outer measures, measurability, and lattice regular measures
نویسندگان
چکیده
منابع مشابه
Characterizations of Outer Measures Associated with Lattice Measures
Let ν be a finite countably subadditive outer measure defined on all subsets of a set X, take a collection C of subsets of X containing X and ∅, we derive an outer measure ρ using ν on sets in C. By applying this general framework on two special cases in which ν = μ′′, one where μ ∈ Mσ(L) and the other where μ ∈ Mσ(L1), L1 ⊆ L2 being lattices on a set X, we obtain new characterizations of the o...
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In this paper we define and discuss the theory of abstract outer measures on a sequentially continuous(2) linear lattice S. This is a generalization of the concept of outer measure on a function space as used by Bourbaki [3]. H. Nakano [7] and M. H. Stone [8] have modernized Lebesgue's extension theory; our approach provides a common generalization of their theories. We show, for example, that ...
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Associated with a 0-1 measure E I(-.) where is a lattice of subsets of X are outer measures/’ and ; associated with a o-smooth 0-1 measure # E Io() is an outer measure " or with Io(.Y’), ’ being the complementary lattice, another outer measure I. These outer measures and their associated measurable sets are used to establish separation properties on o and regularity and a-smoothness of . Separa...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1996
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171296000488