Measure is Finitely Additive Function

Theorem
Let $\mathcal A$ be a $\sigma$-algebra.

Let $\mu: \mathcal A \to \overline {\R}$ be a measure on $\mathcal A$.

Then $\mu$ is finitely additive.

Proof
Follows as a corollary of Countably Additive Function also Finitely Additive.