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Keywords:
finitely additive integration; localized convergence; integral representation; weak continuity conditions; horizontal integration
finitely additive integration; localized convergence; integral representation; weak continuity conditions; horizontal integration
Summary:
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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