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.