A definition of ”monotone integral” is given, for real-valued maps andwith respect to Dedekind complete Riesz space-valued ”capacities”. Some representation theorems are proved; in particular, we give here a version of Riesz representation theorem. Moreover, a concept of weak convergence is introduced, and some Portmanteau-type theorems, Vitali convergence and Fatou theorems are proved. Finally, a version of both strong and weak laws of large numbers is demonstrated.
The monotone integral with respect to Riesz-space valued capacities
BOCCUTO, Antonio;SAMBUCINI, Anna Rita
1996
Abstract
A definition of ”monotone integral” is given, for real-valued maps andwith respect to Dedekind complete Riesz space-valued ”capacities”. Some representation theorems are proved; in particular, we give here a version of Riesz representation theorem. Moreover, a concept of weak convergence is introduced, and some Portmanteau-type theorems, Vitali convergence and Fatou theorems are proved. Finally, a version of both strong and weak laws of large numbers is demonstrated.File in questo prodotto:
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