The Alexandroff theorem for Riesz space-valued non-additive measures

The Alexandroff theorem for a compact non-additive measure with values in a Riesz space is still valid for the following two cases: one is the case that the measure is autocontinuous and the Riesz space has the weak asymptotic Egoroff property and the other is the case that the measure is uniformly autocontinuous and the Riesz space is weakly σ-distributive. A close connection between regularity and continuity of non-additive measures is also given.