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The Nikodým boundedness theorem for lattice-valued measures. (English) Zbl 0661.28003

Let \(\Sigma\) be a \(\sigma\)-algebra of subsets of a set S and X a vector lattice. We give conditions on the lattice X so that a finitely additive set function \(\mu:\Sigma \to X\) (or a family \(M=\{\mu_ i:i\in I\}\) of finitely additive set functions) which is exhaustive with respect to order convergence has order bounded range (M has uniformly order bounded ranges).
Reviewer: Ch.Swartz

MSC:

28B15 Set functions, measures and integrals with values in ordered spaces
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