Real Analysis Exchange

Limits of transfinite convergent sequences of derivatives

Martin Dindoš

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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.

Article information

Real Anal. Exchange, Volume 22, Number 1 (1996), 338-345.

First available in Project Euclid: 1 June 2012

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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]

Transfinite sequences Martin’s axiom Continuum hypothesis.


Dindoš, Martin. Limits of transfinite convergent sequences of derivatives. Real Anal. Exchange 22 (1996), no. 1, 338--345.

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