Outer measures and weak regularity of measures
Summary: This paper investigates smoothness properties of probability measures on lattices which imply regularity, and then considers weaker versions of regularity; in particular, weakly regular, vaguely regular, and slightly regular. They are derived from commonly used outer measures, and we analyze them mainly for the case of \(I({\mathcal L})\) or for those elements of \(I({\mathcal L})\) with added smoothness conditions, where \(I({\mathcal L})\) denotes the algebra of non-trivial zero-one valued finitely additive measures on the algebra \(A({\mathcal L})\) generated by the lattice \({\mathcal L}\) of subsets of an arbitrary set \(X\).
scientific article; zbMATH DE number 733293