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On the Baire class of $ \mathcal{I}$-approximate derivatives


Author: Ewa Łazarow
Journal: Proc. Amer. Math. Soc. 100 (1987), 669-674
MSC: Primary 26A24; Secondary 26A21
DOI: https://doi.org/10.1090/S0002-9939-1987-0894436-6
MathSciNet review: 894436
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Abstract: Basic properties of an $ \mathcal{I}$-approximate derivative which is a category analogue of the approximate derivative were considered in [3]. Using the notion of balanced selection and the result of O'Malley, we shall prove that the $ \mathcal{I}$-approximate derivative is of Baire class one.


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

  • [1] R. J. O'Malley, Selective derivatives, Acta Math. Hungar. 29 (1977).
  • [2] -, Balanced selections, Real Anal. Exchange 8 (1982-83). MR 700201 (85c:26002)
  • [3] E. Łazarow and W. Wilczyński, $ \mathcal{I}$-approximate derivatives (to appear).
  • [4] W. Poreda, E. Wagner-Bojakowska, and W. Wilczyński A category analogue of the density topology, Fund. Math. 128 (1985), 167-173. MR 813753 (87b:54034)

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DOI: https://doi.org/10.1090/S0002-9939-1987-0894436-6
Article copyright: © Copyright 1987 American Mathematical Society

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