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1. The monotone integral with respect to Riesz space-valued capacities

Author

A. BOCCUTO and A.R. SAMBUCINI

Subjects
capacities, integration, representation theorems, convergence in distribution, portmanteau theorem, vitali and fatou convergence theorems, Mathematics, QA1-939
Abstract

A definition of “monotone integral” is given, similarly as in [5], for real-valued maps and with 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.

Published
1996

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