Regularities of Riesz space-valued non-additive measures with applications to convergence theorems for Choquet integrals
A deeper investigation of Radonness and tau-smoothness properties of Riesz space-valued Borel non-additive measures is carried out. To this end, due to a lack of epsilon-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. (C) 2009 Elsevier B.V. All rights reserved.
riesz space-valued non-additive measure multiple egoroff property regularity of measures asymptotic null-additivity total continuity