Hey people. Im sitting here with an assignment.

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It is given that P(A) = P(B) = 0

Then i have to prove that P(A U B) = 0.

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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

and

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.

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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.