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International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 4, Pages 707-724
http://dx.doi.org/10.1155/S0161171287000814

On measure repleteness and support for lattice regular measures

1Department of Mathematics, Polytechnic Institute of New York, Brooklyn, NY 11201, USA
2Department of Mathematics, Long Island University, Brooklyn, NY 11201, USA

Received 31 October 1984

Copyright © 1987 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.

Abstract

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.