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International Journal of Mathematics and Mathematical Sciences
Volume 13, Issue 4, Pages 783-798
http://dx.doi.org/10.1155/S0161171290001090

Induced measures on Wallman spaces

University of Setif, Algeria

Received 14 April 1989; Revised 3 October 1989

Copyright © 1990 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

Let X be an abstract set and 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() and another measure μ on the space IRσ(). 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.