Sunday, April 24, 2016

Nowhere continuous real valued function which has an antiderivative

My question:



Is there a function $f: \mathbb{R} \rightarrow \mathbb{R}$ that nowhere continuous on its domain, but has an antiderivative?




If there is no such a function, is it true to conclude that: to have an antiderivative, $f$ is necessary to be continuous at least at one point on its domain?



Any comments/ inputs are highly appreciated. Thanks in advance.

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