Let X be any nonempty set, A be an algebra of subsets of X, and E be the Stone space associated with A. Let G be a Dedekind complete lattice group and m be a finitely additive positive measure defined on A and with values in G. We prove the existence of the Stone-type extension of m, defined on the whole sigma-algebra of all Borel subsets of E. We use the tools of the transfinite induction and the Maeda-Ogasawara-Vulikh representation theorem for Archimedean lattice groups.
On Stone-type extensions for group-valued measures
BOCCUTO, Antonio
1995
Abstract
Let X be any nonempty set, A be an algebra of subsets of X, and E be the Stone space associated with A. Let G be a Dedekind complete lattice group and m be a finitely additive positive measure defined on A and with values in G. We prove the existence of the Stone-type extension of m, defined on the whole sigma-algebra of all Borel subsets of E. We use the tools of the transfinite induction and the Maeda-Ogasawara-Vulikh representation theorem for Archimedean lattice groups.File in questo prodotto:
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