Vol. 34, No. 2, 1970

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Weak denseness of nonatomic measures on perfect, locally compact spaces

Norman Yeomans Luther

Vol. 34 (1970), No. 2, 453–460
Abstract

Our primary result is that the space of all compact zeroset-regular, nonatomic, countably additive Baire measures is dense, with iespect to the weak topology, in the space of alI finitely additive, zero-set regular Baire measures if the underlying topological space is locally compact, Iiausdorff, and perfect. Moreover, a corresponding result holds for Borel measures. These results yield, as easy corollaries, the existence of nonzero, nonatomic, countably additive, compact-regular Baire and Borel measures on a locally compact, Hausdorff space which contains a nonempty perfect subset, Two converses conclude the paper.

Mathematical Subject Classification
Primary: 28.13
Milestones
Received: 17 October 1969
Published: 1 August 1970
Authors
Norman Yeomans Luther