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

 

Limits of differentiable functions


Author: Udayan B. Darji
Journal: Proc. Amer. Math. Soc. 124 (1996), 129-134
MSC (1991): Primary 26A24, 26A21; Secondary 40A30
MathSciNet review: 1285985
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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: http://dx.doi.org/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
Article copyright: © Copyright 1996 American Mathematical Society