## 7.4. Lebesgue Integral

### Example 7.4.11(c): Properties of the Lebesgue Integral

Suppose

The proof is easy, using one of the properties of the Lebesgue integral ...
so it's of course left as an exercise.
*f*is a bounded, non-negative function defined on a measurable set*with finite measure and***E***is measurable with***F****E***m(*. Then show that*) m(***F***)***E**_{F}f(x) dx_{E}f(x) dx

*Hint:*
*F
(E - F) = E
* and

*and*

**F***are disjoint ...*

**E - F**