On properties of the approximate Peano derivatives

Babcock, Bruce S.

doi:10.1090/S0002-9947-1975-0414803-0

On properties of the approximate Peano derivatives
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by Bruce S. Babcock

Trans. Amer. Math. Soc. 212 (1975), 279-294

DOI: https://doi.org/10.1090/S0002-9947-1975-0414803-0

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Abstract:

The notion of kth approximate Peano differentiation not only generalizes kth ordinary differentiation but also kth Peano differentiation and kth ${L_p}$ differentiation. Recently, M. Evans has shown that a kth approximate Peano derivative at least shares with these other derivatives the property of belonging to Baire class one. In this paper the author extends the properties possessed by a kth approximate Peano derivative by showing that it is like the above derivatives in that it also possesses the following properties: Darboux, Denjoy, Zahorski, and a new property stronger than the Zahorski property, Property Z.

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