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.

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