Riemann Integration 7: Riemann-Lebesgue Theorem Part 2

Set of discontinuities has measure zero implies Riemann integrable. I consider this to be the harder side of the implication, which is why this video is a bit long.

A FEW TYPOS:
On step (5) of the proof, note that it should be "sum over j in C_1 (..) + sum over j in C_2 (..)" not a minus sign. This is around minute 20:30.

Also on step (5) of the proof, when I get the inequality minutes 21-24, I write "union over j of m([y_{r-1}, y_{r}]) ..." This should be "y_{r_{j-1}} - y_{r_j}" where r_j is the r corresponding to j in C_i as per the definition of the C_i.

This is a good reminder: Never trust me 100% and if something seems seriously wrong, consider the possibility that I am wrong! 50-100% of the time that will be the case! Never hesitate to leave comments for clarification!