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

Schaefer, Helmut; Zhang, Xiao-Dong

doi:10.1090/S0002-9939-97-03464-3

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.

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