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Absolute continuity theorems for abstract Riemann integration

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Abstract

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 elemental integrals.

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Authors and Affiliations

  1. Departamento de Álgebra y Análisis Matemático, Universidad de Almería, 04120, Almería, Spain

    E. de Amo & R. del Campo

  2. Departamento de Análisis Matemático, Universidad de Granada, 18071, Granada, Spain

    M. Díaz-Carrillo

Authors
  1. E. de Amo
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  2. R. del Campo
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  3. M. Díaz-Carrillo
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de Amo, E., del Campo, R. & Díaz-Carrillo, M. Absolute continuity theorems for abstract Riemann integration. Czech Math J 57, 793–807 (2007). https://doi.org/10.1007/s10587-007-0076-2

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  • DOI: https://doi.org/10.1007/s10587-007-0076-2

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