International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 4, Pages 707-724
On measure repleteness and support for lattice regular measures
1Department of Mathematics, Polytechnic Institute of New York, Brooklyn 11201, NY, USA
2Department of Mathematics, Long Island University, Brooklyn 11201, NY, USA
Received 31 October 1984
Copyright © 1987 George Bachman and P. D. Stratigos. 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.
The present paper is mainly concerned with establishing conditions which
.assure that all lattice regular measures have additional smoothness properties or
that simply all two-valued such measures have such properties and are therefore Dirac
measures. These conditions are expressed in terms of the general Wallman space. The
general results are then applied to specific topological lattices, yielding new conditions
for measure compactness, Borel measure compactness, clopen measure repleteness,
strong measure compactness, etc. In addition, smoothness properties in the
general setting for lattice regular measures are related to the notion of support,
and numerous applications are given.