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Points of infinite derivative of Cantor functions. (English) Zbl 1120.28009

Summary: 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.

MSC:

28A80 Fractals
28A78 Hausdorff and packing measures
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