Finding the Measure of A, B: Prove m(A)+m(B)=m(AuB)+m(AnB)

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Homework Statement



A, B in a sigma algebra

Prove
m(A)+m(B)=m(AuB)+m(AnB)

m denotes the measure.

The Attempt at a Solution



Don't see how to do it.

Somehow we are dealing with each individual set and taking the measure on them. Then finding what they equate to.
 
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Discussion

A measure is additive on countable disjoint unions. So have you tried to write A[itex]\cup[/itex]B as a union of disjoint sets?

(Note: I'm assuming m is a finite measure, i.e. does not take on infinity.)
 
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Ok you haven't tried hard Pivoxa
Hint:
use [tex]A= [A - (A \cap B)] \cup (A \cap B) \hspace{10pt}\text{or}\hspace{10pt} B= [B - (A \cap B)] \cup (A \cap B)[/tex] and see what you get from it.