Displaying similar documents to “Integral extension with locally-integral seminorm”

Absolute continuity theorems for abstract Riemann integration

E. de Amo, R. del Campo, M. Díaz Carillo (2007)

Czechoslovak Mathematical Journal

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Absolute continuity for functionals is studied in the context of proper and abstract Riemann integration examining the relation to absolute continuity for finitely additive measures and giving results in both directions: integrals coming from measures and measures induced by integrals. To this end, we look for relations between the corresponding integrable functions of absolutely continuous integrals and we deal with the possibility of preserving absolute continuity when extending the...

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.