## $L _{p}$ derivatives and approximate Peano derivatives

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- by Michael J. Evans PDF
- Trans. Amer. Math. Soc.
**165**(1972), 381-388 Request permission

## Abstract:

It is known that approximate derivatives and*k*th Peano derivatives share several interesting properties with ordinary derivatives. In this paper the author points out that

*k*th ${L_p}$ derivatives also share these properties. Furthermore, a definition for a

*k*th approximate Peano derivative is given which generalizes the notions of a

*k*th Peano derivative, a

*k*th ${L_p}$ derivative, and an approximate derivative. It is then shown that a

*k*th approximate Peano derivative at least shares the property of belonging to Baire class one with these other derivatives.

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## Additional Information

- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**165**(1972), 381-388 - MSC: Primary 26A24
- DOI: https://doi.org/10.1090/S0002-9947-1972-0293030-1
- MathSciNet review: 0293030