Question

The Lebesgue Intgeral :
Let f:A-> R be a bounded measurable function on a bounded measurable subset A of R. Suppose that for any epsilon > 0, there exist simple functions f1 and f2 such that f1<=f<=f2 and..

Answer 1

\[\int\limits\limits_{A}^{} f2 dm - \int\limits\limits_{A}^{} f1 dm < \epsilon \]

Answer 2

By letting \[L = \inf \left\{ \int\limits_{A}^{} f2 dm : f2 simple , f \le f2\right\}\]

Answer 3

Show that f is Lebesgue integrable on A.