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Representations of Riesz spaces as spaces of measures. I. (English) Zbl 0803.46008

The author gives a concrete representation for spaces which reflect many properties of duality. Especially he shows that a Riesz space \(E\) can be represented as an order dense Riesz subspace of a band \(M\) of measures iff it is represented by the set \(E^ \pi\) of its order continuous linear forms. \(E\) is an ideal of \(M\) iff \(E\) is Dedekind complete, \(E= M\) iff \(E\) is hypercomplete. The results of the author are also generalizations of some previous results by D. H. Fremlin [Proc. Camb. Philos. Soc. 63, 951-956 (1967; Zbl 0179.170)] and C. Constantinescu [‘Duality in measure theory’, Lecture Notes Math. 796 (1980; Zbl 0429.28009)].

MSC:

46A40 Ordered topological linear spaces, vector lattices
46E27 Spaces of measures
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References:

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