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Decompositions of submeasures. (English) Zbl 0556.28007
The main theorem is a Lebesgue decomposition theorem for exhaustive submeasures with respect to Fréchet-Nikodým topologies. It generalizes Drewnowski’s Lebesgue decomposition for exhaustive submeasures with respect to additivies [L. Drewnowski, Stud. Math. 48, 23-48 (1973; Zbl 0269.28003)] and implies Traynor’s Lebesgue decomposition for exhaustive Fréchet - Nikodým topologies [T. Traynor, Trans. Am. Math. Soc. 220, 307-319 (1976; Zbl 0334.28010)]. Applications to Maharam’s control measure problem are given. Another proof of the main theorem appears in [C. H. Brook and T. Traynor, Univ. of Windsor Mathematics Report 83-14].

MSC:
28A12 Contents, measures, outer measures, capacities
28A60 Measures on Boolean rings, measure algebras
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