Countable subadditivity of a measure
= Countable subadditivity of a measure
= Countable subadditivity
{synonym}
For measurable <sets> $E_n$, a <measure> satisfies
$$
\mu\left(\bigcup_{n\ge1}E_n\right)\le\sum_{n\ge1}\mu(E_n).
$$
Replace $E_n$ by the disjoint <sets> $E_n\setminus\bigcup_{j<n}E_j$, use <countable additivity>, and then monotonicity. The same property is an axiom for an <outer measure> on arbitrary <sets>.