7.1. Riemann Integral
Theorem 7.1.16: Lebesgue's Theorem
f f is a bounded function defined on a closed, bounded interval [a, b] then f is Riemann integrable if and only if the set of points where f is discontinuous has measure zero.
As we will see later, any set of finitely or countably many points is a set of measure zero.
To prove this theorem, we would need to know more about measure theory, which at this point we do not. So, we will postpone this proof.