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Revista de Matemática Teoría y Aplicaciones

Print version ISSN 1409-2433


MONTILLA, Armando. On fubini’s theorem for null sets in vector measures. Rev. Mat [online]. 2017, vol.24, n.2, pp.227-238. ISSN 1409-2433.

In this paper we prove a version of Fubini’s Theorem for null sets in the context of vector measures, in the spirit of the classical proof for sets in the Euclidean plane, namely: Let X and Y be locally compact Hausdorff topological spaces and let µ and νbe regular vector measures on the Baire σ-algebras B0(X) and B0(Y ), respectively. If A C X x Y , then | µ ( ν| (A) = 0 if and only if

| µ | ({x E X: Ax is not a null set}) = 0, where Ax = {y E Y: (x,y) E A}.

Keywords : vector measure; zero measure; product measure; Fubini’s theorem.

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