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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A typical property of Baire $ 1$ Darboux functions


Authors: Michael J. Evans and Paul D. Humke
Journal: Proc. Amer. Math. Soc. 98 (1986), 441-447
MSC: Primary 26A27; Secondary 26A21
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-$ \sigma $-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: http://dx.doi.org/10.1090/S0002-9939-1986-0857937-1
PII: S 0002-9939(1986)0857937-1
Article copyright: © Copyright 1986 American Mathematical Society