Regularities of Riesz space-valued non-additive measures with applications to convergence theorems for Choquet integrals

Authors:
Jun Kawabe
Affiliations:
Department of Mathematics, Faculty of Engineering, Shinshu University, 4-17-1 Wakasato, Nagano 380-8553, Japan
Venue:
Fuzzy Sets and Systems
Year:
2010

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Abstract

A deeper investigation of Radonness and @t-smoothness properties of Riesz space-valued Borel non-additive measures is carried out. To this end, due to a lack of @e-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.