Continuous BA- finitely set function

Abstract

Let ï­ be an BA- finitly additive set function on a measurable space (ï—,F) .
In this paper, we proved the following statement
(1) If ï­ is BA- countably additive, then ï­ is continuous at A for all A F .
(2) If ï­ is - continuous from below at every set A F , then ï­ is BA- countably
additive .
(3) If ï­ is , finitly and continuous from above at ï¦ , then ï­ is BA- countably
additive.