Limits of differentiable functions

Author:
Udayan B. Darji

Journal:
Proc. Amer. Math. Soc. **124** (1996), 129-134

MSC (1991):
Primary 26A24, 26A21; Secondary 40A30

DOI:
https://doi.org/10.1090/S0002-9939-96-02998-X

MathSciNet review:
1285985

Full-text PDF

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].

**1**A. M. Bruckner,*Differentiation of real functions*, Lecture Notes in Math., vol. 659, Springer-Verlag, New York, 1978. MR**80h:26002****2**K. Ciesielski, L. Larson, and K. Ostaszewski, , Mem. Amer. Math. Soc., no. 515, vol. 107, Amer. Math. Soc., Providence, RI, 1994. MR**94f:54035****3**R. Jeffery,*The theory of function of a real variable*, Mathematical Exposition No. 6, University of Toronto Press, Ontario, 1951. MR**13:2166****4**K. Kuratowski,*Topology*, Vol. I, Academic Press, New York, 1966.MR**36:840****5**D. Preiss,*Limits of approximately continuous functions*, Czechoslovak Math. J.**21**(1971), 371--372. MR**44:4154****6**W. Rudin,*Principles of mathematical analysis*, third edition, McGraw-Hill Inc., New York, 1976.MR**52:5893****7**Z. Zahorski,*Sur la premiere derivee*, Trans. Amer. Math. Soc.**69**(1950), 1--54.MR**12:247c**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
26A24,
26A21,
40A30

Retrieve articles in all journals with MSC (1991): 26A24, 26A21, 40A30

Additional Information

**Udayan B. Darji**

Affiliation:
Department of Mathematics University of Louisville Louisville, Kentucky 40292

Email:
ubdarj01@homer.louisville.edu

DOI:
https://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