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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A typical property of Baire $1$ Darboux functions
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by Michael J. Evans and Paul D. Humke PDF
Proc. Amer. Math. Soc. 98 (1986), 441-447 Request permission

Abstract:

It is well known that a real-valued, bounded, Baire class one function of a real variable is the derivative of its indefinite integral at every point except possibly those in a set which is both of measure zero and of first category. In the present paper, a bounded, Darboux, Baire class one function is constructed to have the property that its indefinite integral fails to be differentiable at non-$\sigma$-porous set of points. Such functions are then shown to be "typical" in the sense of category in several standard function spaces.
References
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 98 (1986), 441-447
  • MSC: Primary 26A27; Secondary 26A21
  • DOI: https://doi.org/10.1090/S0002-9939-1986-0857937-1
  • MathSciNet review: 857937