International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 4, Pages 783-798
doi:10.1155/S0161171290001090

Induced measures on Wallman spaces

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.