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Limits of differentiable functions

Author(s): Udayan B. Darji
Journal: Proc. Amer. Math. Soc. 124 (1996), 129-134.
MSC (1991): Primary 26A24, 26A21; Secondary 40A30
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Abstract: Suppose that $\{f_n\}$ is a sequence of differentiable functions defined on [0,1] which converges uniformly to some differentiable function $f$, and $\{f'_n\}$ converges pointwise to some function $g$. Let $M = \{x: f'(x) \neq g(x)\}$. In this paper we characterize such sets $M$ under various hypotheses. It follows from one of our characterizations that $M$ can be the entire interval [0,1].

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Additional Information:

Udayan B. Darji
Affiliation: Department of Mathematics, University of Louisville, Louisville, Kentucky 40292
Email: ubdarj01@homer.louisville.edu

DOI: 10.1090/S0002-9939-96-02998-X
PII: S 0002-9939(96)02998-X
Keywords: $F_\sigma$, $G_{\delta\sigma}$, density topology, approximate continuity, nowhere measure dense
Additional Notes: This is the core part of the author's dissertation which was directed by Professor Jack B. Brown
Communicated by: J. Marshall Ash
Copyright of article: Copyright 1996, American Mathematical Society

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