Limits of transfinite convergent sequences of derivatives

Abstract

The paper solves the question whether the limit of transfinite convergent sequence of derivatives is again the derivative. It shows that this problem cannot be solved in the Zermelo-Fraenkel axiomatic system and that this statement is equivalent to the covering number for Lebesgue null ideal being bigger that \(\aleph_1\). In the second part of the paper author proved an analogue of Preiss’s theorem [P] for the transfinite sequences of derivatives.