Real Analysis Exchange

On the Problem of Characterizing Derivatives

Chris Freiling

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Abstract

We observe how a slight and even natural change in the Kurzweil-Henstock integral leads to a characterization of derivatives. We will also argue that the only way to characterize derivatives is by using some object or procedure which is at least as complicated as an integral.

Article information

Source
Real Anal. Exchange Volume 23, Number 2 (1999), 805-812.

Dates
First available in Project Euclid: 14 May 2012

Permanent link to this document
http://projecteuclid.org/euclid.rae/1337001388

Mathematical Reviews number (MathSciNet)
MR1639989

Zentralblatt MATH identifier
0943.26014

Subjects
Primary: 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15] 26A36: Antidifferentiation 26A3

Keywords
{derivative} {antiderivative} {Kurzweil} {Henstock} {Riemann complete}

Citation

Freiling, Chris. On the Problem of Characterizing Derivatives. Real Analysis Exchange 23 (1999), no. 2, 805--812. http://projecteuclid.org/euclid.rae/1337001388.


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