A finitely additive measure $\mu$ is a measure if and only if it is continuous from below.
I want to know how I should proceed in proving this statement. My idea is to first assume we have a finitely additive measure $\mu$ and then prove that it is continuous from below. Then for the converse assume we have an increasing sequence of sets in $M$ and show that $\mu$ is finitely additive.
I am not sure if this is the correct approach I should take. Any suggestions is greatly appreciated.