Geodesic
Absolute continuity theorems for abstract Riemann integration
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 3, pp. 793-807 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 28C05
Keywords: finitely additive integration; abstract Riemann integration; absolute continuity 
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     author = {Amo, E. de and Campo, R. del and D{\'\i}az-Carrillo, M.},
     title = {Absolute continuity theorems for abstract {Riemann} integration},
     journal = {Czechoslovak Mathematical Journal},
     pages = {793--807},
     year = {2007},
     volume = {57},
     number = {3},
     mrnumber = {2356281},
     zbl = {1174.28015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_3_a1/}
}
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Amo, E. de; Campo, R. del; Díaz-Carrillo, M. Absolute continuity theorems for abstract Riemann integration. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 3, pp. 793-807. http://geodesic.mathdoc.fr/item/CMJ_2007_57_3_a1/