## 7.3. Measures

### Examples 7.3.10(a): Properties of Measure

For any sets*and*

**A***we have:*

**B**and(A) (Bcomp(A)) =BA

*and*

**A****B***are disjoint. Therefore, by additivity of measure we have:*

*comp(***A***)***B**Thereforem(A) + m(Bcomp(A)) = m(B)A

as we had to prove. Ifm(-A) = m(B) - m(AA)B

*then*

**B****A***so that*

**A***=***B****B**m(-A) = m(B) - m(A)B