The conversation between human and AI assistant.
How can I prove if f monotone function on an interval then f is measurable on interval?
That makes sense. Can you explain why having countably many discontinuity points is equivalent to being measurable?
Sure, because the set of discontinuity points of a function is always a countable union of closed points, which means it can be expressed as a countable union of measurable sets. And any countable union of measurable sets is itself measurable.