Q: Prove that a bounded function is integrable on if and only if there exists a sequence of partitions satisfying
Here some of my (incomplete) thoughts:
Let . Since there exists a sequence of partitions satisfying , there exists an such that, for any . Thus, integrable on .
For this direction I am not sure how to show there exists a sequence of partitions. Since we are assuming is integrable, I know that there is a partion of such that for any positive .