On integration with respect to a DT-measure

DT-measures generalize the topological measures of Aarnes. We continue to study an integral of a real-valued continuous function on compact Hausdorff space with respect to a DT-measure and investigate the following: multiplicativity of this integral, (w*)-topology on the family of DT-measures and density of various subfamilies of this space, and also integral as a set function.