Dixmier’s theorem for sequentially order continuous Baire measures on compact spaces
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- by Helmut H. Schaefer and Xiao-Dong Zhang PDF
- Proc. Amer. Math. Soc. 125 (1997), 93-99 Request permission
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.References
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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
- Received by editor(s): May 1, 1995
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 93-99
- MSC (1991): Primary 28A60, 28C15
- DOI: https://doi.org/10.1090/S0002-9939-97-03464-3
- MathSciNet review: 1342045