OUTER MEASURES ASSOCIATED WITH LATTICE MEASURES AND THEIR APPLICATION

CHARLES TRAINA

《International Journal of Mathematics and Mathematical Sciences》 1995卷 (1995/12) Pp. 725-734

https://doi.org/10.1155/S0161171295000937

摘要

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 ∈ M_σ(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

關鍵字

Normal lattice, lattice regular measures, associated outer measures.