A typical property of Baire Darboux functions

Authors:
Michael J. Evans and Paul D. Humke

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

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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--porous set of points. Such functions are then shown to be "typical" in the sense of category in several standard function spaces.

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DOI:
https://doi.org/10.1090/S0002-9939-1986-0857937-1

Article copyright:
© Copyright 1986
American Mathematical Society