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International Journal of Mathematics and Mathematical Sciences
Volume 14, 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 Hindawi Publishing Corporation. 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 σ-smooth measures with respect to the lattice when further conditions on the lattice hold.