概率论：基本测度论——集合函数 (3)

Hello everyone! This is the last lecture on set functions. In this lecture, I mainly prove a theorem on the continuity of the pre-measure, which provides implications between the sigma additivity, sigma sub-additivity, lower semi-continuity, empty continuity, and upper semi-continuity of content. Then content of the theorem is relatively simple, but its proof is somewhat lengthy. I will provide definitions of measurable space, measure space, and probability space, that will be used in the future. Hope you enjoy!