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

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.