According to Wikipedia, G. Choquet has characterized all real functions which, up to a bicontinuous change of variable, have antiderivative as all the Baire 1 functions which send intervals onto connected sets. I am quite confused by this change of variable. It seems quite clear to me that if a function satisfies the two last conditions, the same holds for all its bicontinuous changes of variable. Can I see an example of a function which has antiderivative, but such that a bicontinuous change of variable of it has no antiderivative? I would expect that such a change of variable is not differentiable, but I have a hard time constructing an example. I have searched G. Choquet's work on internet, but I could not find it either. Is there any reasonably good book discussing the matter in sufficient detail?

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