Geodesic
Decompositions of Submeasures
Canadian journal of mathematics, Tome 36 (1984) no. 4, pp. 577-590

Voir la notice de l'article provenant de la source Cambridge University Press

In [4] we showed that one can tell whether a submeasure on a Boolean algebra has a control measure or is pathological by comparing the Fréchet-Nikodym topology it generates to the universal measure topology of Graves. We then wondered if a submeasure could be decomposed into a part with a control measure and a part which is pathological or zero. This led to the problem of finding a Lebesgue decomposition for a submeasure on an algebra of sets with respect to a Fréchet-Nikodym topology.In [6] Drewnowski proved a Lebesgue decomposition theorem for exhaustive submeasures with respect to “additivities” and a similar theorem for exhaustive Fréchet-Nikodym topologies. He asked if an exhaustive Fréchet-Nikodym topology could be decomposed with respect to another Fréchet-Nikodym topology. In [12] Traynor showed that the answer is “yes”. 
Brook, Cecilia H. Decompositions of Submeasures. Canadian journal of mathematics, Tome 36 (1984) no. 4, pp. 577-590. doi: 10.4153/CJM-1984-036-9
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[1] 1. Aleksyuk, V. N., Theorem on the minorant, Math. Notes Acad. Sci. USSR 21 (1977), 336–340. Google Scholar

[2] 2. Brook, C. H., On the universal measure space, J. Math. Anal. Appl. 85 (1982), 584–598. Google Scholar

[3] 3. Brook, C. H., Continuity properties of vector measures, J. Math. Anal. Appl. 86 (1982), 268–280. Google Scholar

[4] 4. Brook, C. H., The control measure problem and the universal measure topology, Rocky Mt. J. Math 13 (1983), 265–272. Google Scholar

[5] 5. Drewnowski, L., Topological rings of sets, continuous set functions, integration I, II, III, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 20 (1972), 269–276, 277–286, 439–445. Google Scholar

[6] 6. Drewnowski, L., Decompositions of set functions, Studia Math. 48 (1973), 23–48. Google Scholar

[7] 7. Drewnowski, L., On control submeasures and measures, Studia Math. 50 (1974), 203–224. Google Scholar

[8] 8. Fremlin, D. H., The control measure problem, (note of March, 1978), University of Essex, Colchester, England. Google Scholar

[9] 9. Graves, W. H., On the theory of vector measures, Amer. Math. Soc. Memoirs 195 (1977). Google Scholar

[10] 10. Maharam, D., An algebraic characterization of measure algebras, Ann. Math. 48 (1947), 154–167. Google Scholar

[11] 11. Traynor, T., S-bounded additive set functions, in Vector and operator-valued measures and applications (Proc. Sympos., Snowbird Resort, Alta, Utah, 1972) (Academic Press, New York), 355–365. Google Scholar

[12] 12. Traynor, T., The Lebesgue decomposition for group-valued set functions, Trans. Amer. Math. Soc 220 (1976), 307–319. Google Scholar

[13] 13. Wilansky, A., Topology for analysis (Ginn, Waltham, Mass., 1970). Google Scholar

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