Interactive Real Analysis
- part of 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
Context
The proof is easy, using one of the properties of the Lebesgue integral ...
so it's of course left as an exercise.
E
is measurable with
m(F) m(E).
Then show that
F f(x) dx
Context
Hint:
F 
(E - F) = E
and
F and E - F are disjoint ...