International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 4, Pages 237-249

Characterizations of outer measures associated with lattice measures

Pao-Sheng Hsu

Department of Mathematics and Statistics, University of Maine, Neville Hall, Orono 04469–5752, Maine, USA

Received 23 April 1999

Copyright © 2000 Pao-Sheng Hsu. 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.


Let ν be a finite countably subadditive outer measure defined on all subsets of a set X, take a collection of subsets of X containing X and , we derive an outer measure ρ using ν on sets in . By applying this general framework on two special cases in which ν=μ, one where μMσ(𝔏) and the other where μMσ(𝔏1),𝔏1𝔏2 being lattices on a set X, we obtain new characterizations of the outer measure μ. These yield useful relationships between various set functions including μi,μj,μ, and μ.