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