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1996/1997 Limits of transfinite convergent sequences of derivatives
Martin Dindoš
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Real Anal. Exchange 22(1): 338-345 (1996/1997).


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.


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Martin Dindoš. "Limits of transfinite convergent sequences of derivatives." Real Anal. Exchange 22 (1) 338 - 345, 1996/1997.


Published: 1996/1997
First available in Project Euclid: 1 June 2012

zbMATH: 0937.26512
MathSciNet: MR1433618

Primary: 40A30 , 46G05
Secondary: 03E50

Keywords: Continuum hypothesis. , Martin’s axiom , Transfinite sequences

Rights: Copyright © 1996 Michigan State University Press

Vol.22 • No. 1 • 1996/1997
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