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 that
F f(x) dx E f(x) dx
Context Context
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 ...

Interactive Real Analysis, ver. 1.9.5
(c) 1994-2007, Bert G. Wachsmuth
Page last modified: Mar 28, 2007