Department of Mathematics, Florida Atlantic University, Boca Raton, Florida 33431
Xiao-Dong Zhang ; Department of Mathematics, Florida Atlantic University, Boca Raton, Florida 33431
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.