Measure is Strongly Additive

Theorem
Let $\left({X, \Sigma, \mu}\right)$ be a measure space.

Then $\mu$ is strongly additive, that is:


 * $\forall E, F \in \Sigma: \mu \left({E \cap F}\right) + \mu \left({E \cup F}\right) = \mu \left({E}\right) + \mu \left({F}\right)$

Proof
Combine Measure is Finitely Additive Function with Additive Function is Strongly Additive.