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.