Absolute continuity theorems for abstract Riemann integration

E. de Amo; R. del Campo; M. Díaz Carillo

Displaying similar documents to “Absolute continuity theorems for abstract Riemann integration”

Abstract Riemann integrability and measurability

E. de Amo, R. del Campo, M. Díaz Carrillo (2009)

Czechoslovak Mathematical Journal

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We prove that the spectral sets of any positive abstract Riemann integrable function are measurable but (at most) a countable amount of them. In addition, the integral of such a function can be computed as an improper classical Riemann integral of the measures of its spectral sets under some weak continuity conditions which in fact characterize the integral representation.

Integral extension with locally-integral seminorm

M. Díaz Carillo, F. Muňoz Rivas (1990)

Acta Universitatis Carolinae. Mathematica et Physica

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Finitely additive integration.

M. Díaz Carrillo, P. Bobillo Guerrero (1987)

Extracta Mathematicae

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On integration of vector functions with respect to vector measures

José Rodríguez (2006)

Czechoslovak Mathematical Journal

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We study integration of Banach space-valued functions with respect to Banach space-valued measures. We focus our attention on natural extensions to this setting of the Birkhoff and McShane integrals. The corresponding generalization of the Birkhoff integral was first considered by Dobrakov under the name $S^{*}$ -integral. Our main result states that $S^{*}$ -integrability implies McShane integrability in contexts in which the later notion is definable. We also show that a function is measurable and...