Hey people. Im sitting here with an assignment.
It is given that P(A) = P(B) = 0
Then i have to prove that P(A U B) = 0.
We are supposed to use the theorem 3.1:
Let P be a probability measure. Then we have that
P(A\B) = P(A) - P(B) if A contains B
P(Ac) = 1 - P(A) where Ac is A complement.
furthermore, P is increasing in the sense that
if A contains B it implies that P(A) is greater than or equal to P(B)
and P is continuous in the sense that An (arrow up) A => P(An) (arrow up) P(A) and the same the other way around.
I hope it makes sense and i hope someone can help me.
Its a fairly simple thing, but somehow i cant wrap my head around it.