We know by Riemann Lebesgue theorem that any bounded funtion $f:[a,b]$$\to R$ is Riemann Integrable if the set of discontinuity of $f$ is a measure zero set.
Now my question is : Is there any function $f$ which is discontinuous on Cantor Set? (Since Cantor Set has measure zero but it's uncountable)
Also I may slightly generalized this as follows:Is there any (class of) funtion(s) which is(are) Riemann Integrable but has discontinuities on an uncountable set(ofc Measure zero)?