$F$ is a finite measure on $(X,A)$
$a$ and $b$ belong to $A$
show that $F(a \cup b)=F(a)+F(b)-F(a \cap b)$
I have no idea how to approach this question. Any assistance would be appreciated.
$F$ is a finite measure on $(X,A)$
$a$ and $b$ belong to $A$
show that $F(a \cup b)=F(a)+F(b)-F(a \cap b)$
I have no idea how to approach this question. Any assistance would be appreciated.
Hint: write $a \cup b$ as the following disjoint union: $ a \cup b = [a - (a \cap b)] \cup (a \cap b) \cup [b - (a \cap b)]. $
Note that $ a = (a\cap b^c) \cup (a \cap b)$
so $F(a)=F(a \cap b^c) + F(a \cap b)$
Also, $a \cup b = (a\cap b^c) \cup b$, so $F(a \cup b)= F(a\cap b^c) + F(b)$. Hence $ F(a \cup b) = ...$