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Proceedings of the American Mathematical Society

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The Baire class of approximate symmetric derivates


Author: Lee Larson
Journal: Proc. Amer. Math. Soc. 87 (1983), 125-130
MSC: Primary 26A24
MathSciNet review: 677247
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Abstract: It is shown that all approximate symmetric derivatives of measurable functions are in Baire class one. Further, if $ f$ is a measurable function which is finite a.e., then its upper and lower approximate symmetric derivates are in Baire class three.


References [Enhancements On Off] (What's this?)

  • [1] C. Goffman, Real functions, Holt, New York, 1964.
  • [2] N. K. Kundu, Symmetric derivatives and approximate symmetric derivatives of continuous functions, Rev. Roumaine Math. Pures Appl. 18 (1973), 689–697. MR 0320241
  • [3] L. Larson, The symmetric derivatives, Trans. Amer. Math Soc. (to appear).
  • [4] David Preiss, Approximate derivatives and Baire classes, Czechoslovak Math. J. 21 (96) (1971), 373–382. MR 0286951

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0677247-2
Keywords: Symmetric derivative, approximate derivative, Baire classes
Article copyright: © Copyright 1983 American Mathematical Society