International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 4, Pages 237-249
Characterizations of outer measures associated with lattice measures
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 be a finite countably subadditive outer measure defined
on all subsets of a set , take a collection of
subsets of containing and , we derive an outer
measure using on sets in . By applying
this general framework on two special cases in which ,
one where and the other where , being lattices on a set
, we obtain new characterizations of the outer measure .
These yield useful relationships between various set functions
including , and .