Abstract
A theorem about the Radon-Nikodym property and the convergence of bounded martingales is proved for a bilinear integral in locally convex spaces.
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A.Balbás, P. JiménezGuerra, Un teorema de Radon-Nikodym para integrales bilineales (A Radon-Nikodym theorem for bilinear integrals),Rev. R. Acad. Ci. Madrid 78 (1984) 217–220.MR 87b: 46048
A.Balbás, P. JiménezGuerra, A Radon-Nikodym theorem for a bilinear integral in locally convex spaces,Math. Japonica 32 (1987) 863–870.MR 89f: 46096
R. G.Bartle, A general bilinear vector integral,Studia Math. 15 (1956) 337–352.MR 18, 289
J. Diestel, J. J. Uhl, Vector measures,Math. Surveys 15 Providence R. I., 1977,MR 56: 12216
I.Dobrakov, On integration in Banach spaces, I,Czech. Math. J. 20 (1970) 511–536.MR 51: 1391
F. J. Fernández Fernández-Arroyo, producto de medidas valoradas en espacios localmente convexos (Product of measures with values in locally convex spaces),Ph. D. Thesis. U. N. E. D. Madrid, 1987.
P. JiménezGuerra, Derivación de medidas e integración vectorial bilinear, (Derivation of measures and bilinear vectorial integration),Rev. R. Acad. Ci. Madrid82 (1988) 115–128.
H. B.Maynard, A Radon-Nikodym theorem for operator valued measures,Trans. Amer. Math. Soc. 173 (1972) 449–463.MR 46: 9289
R. RaoChivukula, A. S.Sastry, Product vector measures via Bartle integrals,J. Math. Anal. Appl. 96 (1983) 180–195.MR 85h: 28007
S. Rodríguez Salazar, Integración general en espacios localmente convexos,Ph. D. Thesis. Madrid 1985.
B.Rodríguez-Salinas, Integración de funciones con valores en un espacio localmente convexo,Rev. R. Acad. Ci. Madrid 73 (1979) 361–387.MR 82i: 46061
B.Rodríguez-Salinas, La propiedad de Radon-Nikodym, δ-dentabilidady martingalas en espacios localmente convexos (The Radon-Nikodym property, δ-dentability and martingales in locally convex spaces),Rev. R. Acad. Ci. Madrid 74 (1980) 65–89.MR 82i: 46063
S. A. Sivasankara, Vector integrals and product of vector measures,Ph. D. Thesis. Univ. Microfilm Inter. Michigan (1983).
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Fernández, F.J., Guerra, P.J. On the Radon-Nikodym property for operator valued measures. Period Math Hung 22, 147–151 (1991). https://doi.org/10.1007/BF01960504
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DOI: https://doi.org/10.1007/BF01960504