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The Denjoy-Clarkson property with respect to Hausdorff measures for the gradient mapping of functions of several variables. (English) Zbl 1154.26016
Summary: We construct a differentiable function \(f:\mathbb{R}^{^{ n }}\rightarrow \mathbb{R}\) \((n\geq 2)\) such that the set \((\nabla f)^{-1}(B(0,1))\) is a nonempty set of Hausdorff dimension 1. This answers a question posed by Z. Buczolich [Rev. Mat. Iberoam. 21, 889–910 (2005; Zbl 1116.26007)].

MSC:
26B05 Continuity and differentiation questions
28A75 Length, area, volume, other geometric measure theory
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References:
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