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Transactions of the American Mathematical Society

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The Lebesgue decomposition for group-valued set functions

Author: Tim Traynor
Journal: Trans. Amer. Math. Soc. 220 (1976), 307-319
MSC: Primary 28A45
MathSciNet review: 0419725
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Abstract: A Lebesgue-type decomposition is obtained for finitely additive set functions on a ring with values in topological groups. Corresponding results for Fréchet-Nikodým topologies are included. This generalizes Darst's result for real-valued set functions and a result of Drewnowski.

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Keywords: Lebesgue decomposition, Hewitt-Yosida decomposition, vector measures, group-valued measures, finitely additive set functions, Fréchet-Nikodým topologies
Article copyright: © Copyright 1976 American Mathematical Society