I am reading this answer: https://math.stackexchange.com/a/246469/1078713.
And I understand everything except how to prove that $P$ is pre-measure.
Specifically I can't prove that if countable (infinite) pairwise disjoint sets from algebra of finite unions of measurable rectangles is in this algebra (is of the form of finite union of measurable rectangles) then $P$ is countable (infinite) additive.
How to prove it?
