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 μ⌢ 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 μ⌢, μ˜ and μ′; and try to set some new criterion for repleteness and measure repleteness.