Limits of differentiable functions

Darji, Udayan

doi:10.1090/S0002-9939-96-02998-X

Limits of differentiable functions
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by Udayan B. Darji PDF

Proc. Amer. Math. Soc. 124 (1996), 129-134 Request permission

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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