Real Analysis Exchange
- Real Anal. Exchange
- Volume 22, Number 1 (1996), 338-345.
Limits of transfinite convergent sequences of derivatives
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.
Real Anal. Exchange, Volume 22, Number 1 (1996), 338-345.
First available in Project Euclid: 1 June 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 40A30: Convergence and divergence of series and sequences of functions 46G05: Derivatives [See also 46T20, 58C20, 58C25]
Secondary: 03E50: Continuum hypothesis and Martin's axiom [See also 03E57]
Dindoš, Martin. Limits of transfinite convergent sequences of derivatives. Real Anal. Exchange 22 (1996), no. 1, 338--345. https://projecteuclid.org/euclid.rae/1338515225