Interactive Real Analysis
- part of Examples 7.1.17(a):
Show that every monotone function defined on [a, b]
is Riemann integrable.
Back
We have shown before that a
monotone function f defined on a closed interval
[a, b] has at most countably many discontinuities.
BackTherefore such a function f is continuous except at countably many points, so that by our previous theorem the function must be Riemann integrable.