On regular and sigma-smooth two valued measures and lattice generated topologies

Robert W. Shutz

International Journal of Mathematics and Mathematical Sciences, 1993, vol. 16, 1-8

Abstract:

Let X be an abstract set and L a lattice of subsets of X . I ( L ) denotes the non-trivial zero one valued finitely additive measures on A ( L ) , the algebra generated by L , and I R ( L ) those elements of I ( L ) that are L -regular. It is known that I ( L ) = I R ( L ) if and only if L is an algebra. We first give several new proofs of this fact and a number of characterizations of this in topologicial terms.

Next we consider, I ( σ * , L ) the elements of I ( L ) that are σ -smooth on L , and I R ( σ , L ) those elements of I ( σ * , L ) that are L -regular. We then obtain necessary and sufficent conditions for I ( σ * , L ) = I R ( σ , L ) , and in particuliar ,we obtain conditions in terms of topologicial demands on associated Wallman spaces of the lattice.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:517474

DOI: 10.1155/S0161171293000031

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