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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

On properties of the approximate Peano derivatives


Author: Bruce S. Babcock
Journal: Trans. Amer. Math. Soc. 212 (1975), 279-294
MSC: Primary 26A24
MathSciNet review: 0414803
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0414803-0
PII: S 0002-9947(1975)0414803-0
Keywords: Approximate derivatives, approximate Peano derivatives, Baire class one, Darboux property, Denjoy property, Zahorski property, Property Z
Article copyright: © Copyright 1975 American Mathematical Society