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Abstract Riemann integrability and measurability

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Abstract

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.

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Authors and Affiliations

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

    E. de Amo & R. del Campo

  2. Dpto. de Ánalisis 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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Correspondence to R. del Campo.

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de Amo, E., del Campo, R. & Díaz Carrillo, M. Abstract Riemann integrability and measurability. Czech Math J 59, 1123–1139 (2009). https://doi.org/10.1007/s10587-009-0080-9

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  • DOI: https://doi.org/10.1007/s10587-009-0080-9

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