The Monotone Convergence Theorem | Consequences | Measure Theory

[@Problemathic]

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[@islamatef2526]

I have a question
If we have a function f such that f is not continuous a.e
It is equivalent that f is not measurable ?

[@Problemathic]

Sorry I saw this a bit late. Not necessarily: The Dirichlet function, that has value 0 for rationals and 1 for irrationals, is discontinuous everywhere (and therefore also a.e.) but it is measurable. In fact, its integral is 1

[@islamatef2526]

@@Problemathic thanks 😊 ❤️❤️👍