Measure is Strongly Additive

Theorem
Let $\struct {X, \Sigma, \mu}$ be a measure space.

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


 * $\forall E, F \in \Sigma: \map \mu {E \cap F} + \map \mu {E \cup F} = \map \mu E + \map \mu F$

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