7.4. Lebesgue Integral

Example 7.4.11(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 that
F f(x) dx E f(x) dx
The proof is easy, using one of the properties of the Lebesgue integral ... so it's of course left as an exercise.

Hint: F (E - F) = E and F and E - F are disjoint ...

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