International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 4, Pages 795-804

Special measures and repleteness

El-Bachir Yallaoui

Department of Mathematics, Polytechnic University, Six Metro Tech Center, Brooklyn 11201, NY, USA

Received 14 November 1989; Revised 1 February 1990

Copyright © 1993 El-Bachir Yallaoui. 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 X be an abstract set and a lattice of subsets of X. To each lattice-regular measure μ, we associate two induced measures μ and μ˜ on suitable lattices of the Wallman space IR() and another measure μ on the space IRσ(). We will investigate the reflection of smoothness properties of μ onto μ, μ˜ and μ; and try to set some new criterion for repleteness and measure repleteness.