G. Petruska

Derivatives take every value on the set of approximate continuity points

Here ~ may denote the Banach space of bounded functions consisting of Baire 1 functions, Darboux Baire 1 functions, derivatives or approximately continuous functions. In the first two classes the same result holds also for rngflaf . The behaviour of bounded derivatives on Ay remained open. I mentioned the problem whether r n g f l a f = r n g f holds for typical fEbA (bounded derivatives) on the Lodz summer school on real analysis (1981), and it was answered by D. Preiss affirmatively (communicated in a private letter). In this paper we are going to prove that this result is more than typical, it holds for every fEbA, moreover for every derivative.