The conversation between human and AI assistant.
How can I prove if f monotone function on an interval then f is measurable on interval?
I see. Now, can you tell me why a monotone function can only have countably many discontinuity points?
Yes, because a monotone function can have at most a countable number of discontinuity points, since the set of discontinuity points of a monotone function is always either finite or countable. This is because a monotone function can only have jump discontinuities, which means it can only have finitely many discontinuities of the first kind, plus at most countably many discontinuities of the second kind.