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 | References | Similar Articles | Additional Information

Abstract: Suppose that is a sequence of differentiable functions defined on [0,1] which converges uniformly to some differentiable function , and converges pointwise to some function . Let . In this paper we characterize such sets under various hypotheses. It follows from one of our characterizations that 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

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