Finitely additive integration and local integration with respect to upper integrals |
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Authors: | E De Amo R Del Campo M Díaz Carrillo |
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Institution: | (1) Dpto. de álgebra y Análisis Matemático, Universidad de Almería, 04120 Almería, Spain;(2) Dpto. de álgebra y Análisis Matemático, Universidad de Almería, 04120 Almería, Spain;(3) Dpto. de Análisis Matemático, Universidad de Granada, 18071 Granada, Spain |
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Abstract: | Summary We study the integration theory for general integral metrics when restricted to upper integrals q, finding improvements in the relation between the classes of the q-integrable and the ql-integrable functions. We give new results and notions which lead to the desirable characterizations of q-integrable functions as ql-integrable f with q(|f|) < ∞, and of ql-integrable functions via the integrability of their upper truncations, under natural conditions which are fulfilled in most
finitely additive integration theories. |
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Keywords: | finitely additive integration upper integral strong measurability integral metric |
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