International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 4, Pages 725-734

Outer measures associated with lattice measures and their application

Charles Traina

St. John's University, Department of Mathematics & Computer Science, Jamaica 11439, NY, USA

Received 18 March 1994; Revised 7 July 1994

Copyright © 1995 Charles Traina. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Consider a set X and a lattice of subsets of X such that ϕ, X. M() denotes those bounded finitely additive measures on A() which are studied, and I() denotes those elements of M() which are 01 valued. Associated with a μM() or a μMσ() (the elements of M() which are σ-smooth on ) 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 01 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 01 valued measures more refined notions of regularity can be introduced which have no immediate analogues in the general case.