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I am studying the characterization of derivatives in real analysis. I already know that if a function $f$ is a derivative of some function $F$, it must satisfy two conditions:

1.It must have the Darboux Property (Intermediate Value Property).

2.It must be a Baire Class 1 function.

However, I know these two conditions combined are not sufficient.

I came across this paper: Darboux Functions of Baire Class One and Derivatives by Neugebauer (1962)

I am having trouble understanding the logical flow (proof strategy) presented in this paper. The conditions derived seem quite complex.

My Questions:

1.Could someone explain the intuition behind the necessary and sufficient condition provided in this paper?

2.Is there a more modern or "simpler" form of the necessary and sufficient condition for a function to be a derivative?Thank you!

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