Geodesic
A Lebesgue Decomposition for Vector Valued Additive Set Functions Defined on a Lattice
Canadian journal of mathematics, Tome 29 (1977) no. 2, pp. 295-298

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

Our aim is to establish the Lebesgue decomposition for s-bounded vector valued additive functions defined on lattices of sets in both the finitely and countably additive setting. Strongly bounded (s-bounded) set functions were first studied by Rickart [15], and then by Rao [14], Brooks [1] and Darst [5; 6]. In 1963 Darst [6] established a result giving the decomposition of s-bounded elements in a normed Abelian group with respect to an algebra of projection operators. 
Dence, Thomas P. A Lebesgue Decomposition for Vector Valued Additive Set Functions Defined on a Lattice. Canadian journal of mathematics, Tome 29 (1977) no. 2, pp. 295-298. doi: 10.4153/CJM-1977-032-1
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[1] 1. Brooks, James, On the existence of a control measure for strongly bounded vector measures, Bull. Amer. Math. Soc. 77 (1971), 999–1001. Google Scholar

[2] 2. Brunk, H. D., Best fit to a random variable by a random variable measurable with respect to a a-lattice, Pac. J. Math. 11 (1961), 785–802. Google Scholar

[3] 3. Brunk, H. D. Conditional expectation given a a-lattice and applications, Ann. Math. Statist. 36 (1965), 1339–1350. Google Scholar

[4] 4. Brunk, H. D. and Johansen, S., A generalized Radon-Nikodym derivative, Pac. J. Math. 84 (1970), 585–617. Google Scholar

[5] 5. Darst, R. B., A decomposition for complete normed Abelian groups with applications to spaces of additive set functions, Trans. Amer. Soc, 103 (1962), 545–559. Google Scholar

[6] 6. Darst, R. B. The Lebesgue decomposition, Duke Math. J. 30 (1963), 553–556. Google Scholar

[7] 7. Darst, R. B. The Lebesgue decomposition for lattices of projection operators, Advances in Math. 17 (1975), 30–33. Google Scholar

[8] 8. Darst, R. B. and DeBoth, G. A., Two approximation properties and a Radon-Nikodym derivative for lattices of sets, Indiana U. Math. J. 21 (1971), 47–58. Google Scholar

[9] 9. Darst, R. B. and DeBoth, G. A. Norm convergence of martingales of Radon-Nikodym derivatives given a a-lattice, Pac. J. Math. 40 (1972), 547–552. Google Scholar

[10] 10. Drewnowski, L., Decompositions of set functions, Studia Math. 48 (1973), 218–231. Google Scholar

[11] 11. Halmos, Paul, Measure theory (Van Nostrand, 1950). Google Scholar

[12] 12. Johansen, S., The descriptive approach to the derivative of a set function with respect to a a-lattice, Pac. J. Math. 21 (1967), 49–58. Google Scholar

[13] 13. Pettis, B. J., On the extension of measures, Annals of Math. 54 (1951). 186–197. Google Scholar

[14] 14. Rao, M. M., Decomposition of vector measures, Proc. Nat. Acad. Sci. USA 51 (1964), 771–774. Google Scholar

[15] 15. Rickart, C. E., Decomposition of additive set functions, Duke Math. J. 10 (1943), 653–665. Google Scholar

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