Measure is Finitely Additive Function

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Theorem

Let $\Sigma$ be a $\sigma$-algebra on a set $X$.

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


Then $\mu$ is finitely additive.


Proof

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

$\blacksquare$


Sources