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

DOI:
https://doi.org/10.1090/S0002-9939-97-03464-3

MathSciNet review:
1342045

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-97-03464-3

Received by editor(s):
May 1, 1995

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1997
American Mathematical Society