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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Dixmier's theorem for sequentially
order continuous Baire measures
on compact spaces


Authors: Helmut H. Schaefer and Xiao-Dong Zhang
Journal: Proc. Amer. Math. Soc. 125 (1997), 93-99
MSC (1991): Primary 28A60, 28C15
MathSciNet review: 1342045
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Abstract: We prove that a Baire measure (or a regular Borel measure) on a compact Hausdorff space is sequentially order continuous as a linear functional on the Banach space of all continuous functions if and only if it vanishes on meager Baire subsets, a result parallel to a much earlier theorem of Dixmier. We also give some results on the relation between sequentially order continuous measures on compact spaces and countably additive measures on Boolean algebras.


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Additional Information

Helmut H. Schaefer
Affiliation: Department of Mathematics, Florida Atlantic University, Boca Raton, Florida 33431

Xiao-Dong Zhang
Affiliation: Department of Mathematics, Florida Atlantic University, Boca Raton, Florida 33431
Email: x_zhang@acc.fau.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03464-3
PII: S 0002-9939(97)03464-3
Received by editor(s): May 1, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society