Abstract
In this paper, X denotes an arbitrary nonempty set, β a lattice of subsets of X with β , X β β, A(β) is the algebra generated by β and M(β) is the set of nontrivial, finite, and finitely additive measures on A(β), and MR(β) is the set of elements of M(β) which are ββregular. It is well known that any ΞΌ β M(β) induces a finitely additive measure on an associated Wallman space. Whenever is countably additive.We consider the general problem of given ΞΌ β MR(β), how do properties of imply smoothness properties of ΞΌ? For instance, what conditions on are necessary and sufficient for ΞΌ to be Οβsmooth on β, or strongly Οβsmooth on β, or countably additive? We consider in discussing these questions either of two associated Wallman spaces.
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