We prove some convergence theorems for the Kurzweil-Henstock integral in Riesz spaces, for functions defined in an abstract compact topological space with respect to Riesz space-valued measures, which can be unbounded. In particular, some versions of monotone and Lebesgue dominated convergence theorems and Saks-Henstock Lemma are proved.
The Kurzweil-Henstock Integral for Riesz Space-Valued Maps Defined in Abstract Topological Spaces and Convergence Theorems
BOCCUTO, Antonio;
2006
Abstract
We prove some convergence theorems for the Kurzweil-Henstock integral in Riesz spaces, for functions defined in an abstract compact topological space with respect to Riesz space-valued measures, which can be unbounded. In particular, some versions of monotone and Lebesgue dominated convergence theorems and Saks-Henstock Lemma are proved.File in questo prodotto:
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