## Real Analysis Exchange

### Limits of transfinite convergent sequences of derivatives

Martin Dindoš

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 1 June 2012

https://projecteuclid.org/euclid.rae/1338515225

Mathematical Reviews number (MathSciNet)
MR1433618

Zentralblatt MATH identifier
0937.26512

#### Citation

Dindoš, Martin. Limits of transfinite convergent sequences of derivatives. Real Anal. Exchange 22 (1996), no. 1, 338--345. https://projecteuclid.org/euclid.rae/1338515225

#### References

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