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

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
Received: 17 October 1969
Published: 1 August 1970
Norman Yeomans Luther