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Examples 7.3.10(a): Properties of Measure

Show that for any two sets A and B we have that
m(A - B) = m(A) - m(A B)
What if B A?
For any sets A and B we have:
(A B) (A comp(B)) = A
and A B and A comp(B) are disjoint. Therefore, by additivity of measure we have:
m(A B) + m(A comp(B)) = m(A)
Therefore
m(A - B) = m(A) - m(A B)
as we had to prove. If B A then A B = B so that
m(A - B) = m(A) - m(B)
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