International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 1, Pages 93-98
On maximal measures with respect to a lattice
Jersey City State College, 2039 Kennedy Boulevard, Jersey City 07305, NJ, USA
Received 17 November 1988
Copyright © 1991 James Camacho. 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.
Outer measures are used to obtain measures that are maximal with respect to
a normal lattice. Alternate proofs are then given extending the measure theoretic
characterizations of a normal lattice to an arbitrary, non-negative finitely additive
measure on the algebra generated by the lattice. Finally these general results are
used to consider -smooth measures with respect to the lattice when further conditions
on the lattice hold.