Geodesic
Abstract Riemann integrability and measurability
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 4, pp. 1123-1139

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
Classification : 26A42, 28C05
Keywords: finitely additive integration; localized convergence; integral representation; weak continuity conditions; horizontal integration 
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     author = {de Amo, E. and del Campo, R. and Carrillo, M. D{\'\i}az},
     title = {Abstract {Riemann} integrability and measurability},
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     zbl = {1224.28030},
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     url = {http://geodesic.mathdoc.fr/item/CMJ_2009__59_4_a20/}
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de Amo, E.; del Campo, R.; Carrillo, M. Díaz. Abstract Riemann integrability and measurability. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 4, pp. 1123-1139. http://geodesic.mathdoc.fr/item/CMJ_2009__59_4_a20/