# Measure space

1. Aug 5, 2007

### pivoxa15

1. The problem statement, all variables and given/known data

A, B in a sigma algebra

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

m denotes the measure.

3. 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.

2. Aug 5, 2007

### morphism

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

(Note: I'm assuming m is a finite measure, i.e. does not take on infinity.)

Last edited: Aug 5, 2007
3. Aug 12, 2007

### Super_Leunam

Ok you haven't tried hard Pivoxa
Hint:
use $$A= [A - (A \cap B)] \cup (A \cap B) \hspace{10pt}\text{or}\hspace{10pt} B= [B - (A \cap B)] \cup (A \cap B)$$ and see what you get from it.