Interactive Real Analysis
- part of Example 7.3.1(c): Oddities of Riemann Integral
What is the difference between Riemann integrable functions and bounded
continuous functions?
Back
There's little difference. A (bounded) Riemann integrable
function must be continuous except possibly at countably many points.
Therefore bounded functions that are Riemann integrable and those that
are continuous can differ at most at countably many points.
BackThat's odd: if there's little difference between these concepts, why are there two different concepts? Isn't one superfluous?