i've done lebesgue vitali theorem and i'm looking for some examples of Riemann integrable function that is discontinous in a dense set. I'm thinking about caratheristic function but i cannot prove continuity. Any idea?
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@geetha290krm cantor set is not dense – Alessandro Vagni Mar 06 '24 at 08:15
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Thomae's function. See https://math.stackexchange.com/questions/2355570/show-that-f-is-discontinuous-at-every-rational-and-continuous-at-every-irrationa – geetha290krm Mar 06 '24 at 08:22