Proceedings of the American Mathematical Society

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

Author(s): Helmut H. Schaefer; Xiao-Dong Zhang
Journal: Proc. Amer. Math. Soc. 125 (1997), 93-99.
MSC (1991): Primary 28A60, 28C15
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 28A60, 28C15

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: 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
Copyright of article: Copyright 1997, American Mathematical Society

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