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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
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:
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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