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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

$ L\,\sb{p}$ derivatives and approximate Peano derivatives


Author: Michael J. Evans
Journal: Trans. Amer. Math. Soc. 165 (1972), 381-388
MSC: Primary 26A24
MathSciNet review: 0293030
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Abstract: It is known that approximate derivatives and kth Peano derivatives share several interesting properties with ordinary derivatives. In this paper the author points out that kth $ {L_p}$ derivatives also share these properties. Furthermore, a definition for a kth approximate Peano derivative is given which generalizes the notions of a kth Peano derivative, a kth $ {L_p}$ derivative, and an approximate derivative. It is then shown that a kth approximate Peano derivative at least shares the property of belonging to Baire class one with these other derivatives.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0293030-1
Keywords: Peano derivatives, $ {L_p}$ derivatives, approximate derivatives, approximate Peano derivatives, Baire class one, Darboux property, Denjoy property, Zahorski property
Article copyright: © Copyright 1972 American Mathematical Society