International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 4, Pages 783-798
doi:10.1155/S0161171290001090
Induced measures on Wallman spaces
University of Setif, Algeria
Received 14 April 1989; Revised 3 October 1989
Copyright © 1990 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.
Abstract
Let X be an abstract set and ℒ a lattice of subsets of X. To each lattice-regular measure μ, we associate two induced measures μˆ and μ˜ on suitable lattices of the Wallman space IR(ℒ) and another measure μ′ on the space IRσ(ℒ). We will investigate the reflection of smoothness properties of μ onto μˆ, μ˜ and μ′ and try to set some new criterion for repleteness and measure repleteness.