On unilateral and bilateral 𝑛th Peano derivatives

Laczkovich, M.; Preiss, D.; Weil, C.

doi:10.1090/S0002-9939-1987-0866442-9

On unilateral and bilateral $n$th Peano derivatives
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by M. Laczkovich, D. Preiss and C. Weil

Proc. Amer. Math. Soc. 99 (1987), 129-134

DOI: https://doi.org/10.1090/S0002-9939-1987-0866442-9

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Abstract:

A valid proof is given of the assertion that an $n$th Peano derivative that is allowed to attain infinite values is still a function of Baire class one. Also, it is shown that a finite, unilateral $n$th Peano derivative is a function of Baire class one. Finally, an example is given that if infinite values are allowed (actually just $+ \infty$) a unilateral $n$th Peano derivative need not be of Baire class one.

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