Monotonicity and countable subadditivity of measures

Let \((X, \mcm, \mu)\) be a measure space.

1. (Monotonicity) If \(E,F\in\mcm\) and \(E \subseteq F\), then \(\mu(E) \leq \mu(F)\).

2. (Countable subadditivity) If \(E_k\in\mcm\) for \(k\geq1\), then \[ \mu\qty{\bigcup_{k\geq 1} E_k} \leq \sum_{k\geq 1} \mu(E_k). \]