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Regularities of Riesz space-valued non-additive measures with applications to convergence theorems for Choquet integrals. (English) Zbl 1183.28032
Summary: A deeper investigation of Radonness and τ-smoothness properties of Riesz space-valued Borel non-additive measures is carried out. To this end, due to a lack of ε-argument in a Riesz space, the multiple Egoroff property is introduced and enforced on the involved Riesz space. The established regularity properties of Borel non-additive measures are instrumental when formulating certain types of monotone convergence theorems for Choquet integrals.
MSC:
28E10Fuzzy measure theory
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