Example 7.4.10(c): Properties of the Lebesgue Integral
Suppose f is a bounded, non-negative function defined on a measurable set E with finite measure and F E is measurable with m(F) m(E). Then show thatThe proof is easy, using one of the properties of the Lebesgue integral ... so it's of course left as an exercise.
F f(x) dx E f(x) dx
Hint: F (E - F) = E and F and E - F are disjoint ...