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2006/2007 Points of infinite derivative of Cantor functions
Wenxia Li
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Real Anal. Exchange 32(1): 87-96 (2006/2007).


We consider self-similar Borel probability measures $\mu $ on a self-similar set $E$ with strong separation property. We prove that for any such measure $\mu $ the derivative of its distribution function $F(x)$ is infinite for $\mu $-a.e. $x\in E$, and so the set of points at which $F(x)$ has no derivative, finite or infinite is of $\mu $-zero.


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Wenxia Li. "Points of infinite derivative of Cantor functions." Real Anal. Exchange 32 (1) 87 - 96, 2006/2007.


Published: 2006/2007
First available in Project Euclid: 17 July 2007

zbMATH: 1120.28009
MathSciNet: MR2329224

Primary: 28A78 , 28A80

Keywords: Cantor functions , non-differentiability , self-similar measures , self-similar sets

Rights: Copyright © 2006 Michigan State University Press

Vol.32 • No. 1 • 2006/2007
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