In this paper we extend to such spaces the monotone integral, given by Choquetin 1953, and developed by De Giorgi-Letta (1977), Greco (1981), Brooks-Martellotti, and others. Given a mean μ : A --> R and a measurable function f : X-->IR^+_0 , we say that f is integrable (in the monotone sense) if there exists in R the limit (o) − lim_{a--> infty} int_0^a μ({x in X : f(x) > t}) dt. For this integral we obtain some elementary properties and we give some Vitali-type theorems. Finally, we prove a version of Radon-Nikodym-type theorems for the introduced integral.
On the De Giorgi-Letta integral with respect to means with values in Riesz spaces
BOCCUTO, Antonio;SAMBUCINI, Anna Rita
1996
Abstract
In this paper we extend to such spaces the monotone integral, given by Choquetin 1953, and developed by De Giorgi-Letta (1977), Greco (1981), Brooks-Martellotti, and others. Given a mean μ : A --> R and a measurable function f : X-->IR^+_0 , we say that f is integrable (in the monotone sense) if there exists in R the limit (o) − lim_{a--> infty} int_0^a μ({x in X : f(x) > t}) dt. For this integral we obtain some elementary properties and we give some Vitali-type theorems. Finally, we prove a version of Radon-Nikodym-type theorems for the introduced integral.File in questo prodotto:
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