## Real Analysis Exchange

### On the Derivatives of Functions of Bounded Variation

F. S. Cater

#### Abstract

Using a standard complete metric $w$ on the set $F$ of continuous functions of bounded variation on the interval $[0,1]$, we find that a typical function in $F$ has an infinite derivative at continuum many points in every subinterval of $[0,1]$. Moreover, for a typical function in $F$, there are continuum many points in every subinterval of $[0,1]$ where it has no derivative, finite nor infinite. The restriction of the derivative of a typical function in $F$ to the set of points of differentiability has infinite oscillation at each point of this set.

#### Article information

Source
Real Anal. Exchange, Volume 26, Number 2 (2000), 923-932.

Dates
First available in Project Euclid: 27 June 2008

https://projecteuclid.org/euclid.rae/1214571382

Mathematical Reviews number (MathSciNet)
MR1844408

Zentralblatt MATH identifier
1012.26005

#### Citation

Cater, F. S. On the Derivatives of Functions of Bounded Variation. Real Anal. Exchange 26 (2000), no. 2, 923--932. https://projecteuclid.org/euclid.rae/1214571382

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