Lattice separation, coseparation and regular measures

International Journal of Mathematics and Mathematical Sciences. 1996;19(4):773-779 DOI 10.1155/S016117129600107X

 

Journal Homepage

Journal Title: International Journal of Mathematics and Mathematical Sciences

ISSN: 0161-1712 (Print); 1687-0425 (Online)

Publisher: Hindawi Publishing Corporation

LCC Subject Category: Science: Mathematics

Country of publisher: Egypt

Language of fulltext: English

Full-text formats available: PDF, HTML, ePUB

 

AUTHORS

Maurice C. Figueres (The Rockefeller Group, 1230 Avenue of the Americas, New York 10020-1579, NY, USA)

EDITORIAL INFORMATION

Blind peer review

Editorial Board

Instructions for authors

Time From Submission to Publication: 17 weeks

 

Abstract | Full Text

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.