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First Alexandroff Decomposition Theorem for Topological Lattice Group Valued Measures

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Abstract

Let (X, F) be an Alexandroff space, let A(F) be the Boolean subalgebra of 2X generated by F, let G be a Hausdorff commutative topological lattice group and let rbaF(A(F), G) denote the set of all order bounded F-inner regular finitely additive set functions from A(F) into G. Using some special properties of the elements of rbaF(A(F), G), we extend to this setting the first decomposition theorem of Alexandroff.

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Morales, P., Mazarío, F.G. & Guerra, P.J. First Alexandroff Decomposition Theorem for Topological Lattice Group Valued Measures. Order 17, 43–60 (2000). https://doi.org/10.1023/A:1006436305188

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