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

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..

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Show that f is Lebesgue integrable on A.