A singular function with a non-zero finite derivative on a dense set with Hausdorff dimension one

DOI10.1016/j.jmaa.2015.09.036zbMath1326.28006OpenAlexW1753216060MaRDI QIDQ890530

Jaume Paradís, Pelegrí Viader, Manuel Díaz-Carrillo, Juan Fernández-Sánchez

Publication date: 10 November 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2015.09.036

zbMATH Keywords

Hausdorff dimensionsingular functionsCantor functions

Mathematics Subject Classification ID

Length, area, volume, other geometric measure theory (28A75) Hausdorff and packing measures (28A78)

Related Items (6)

On the set of points at which an increasing continuous singular function has a nonzero finite derivative ⋮ Pisot numbers and strong negations ⋮ On the rôle of singular functions in extending the probabilistic symbol to its most general class ⋮ Singular distribution functions for random variables with stationary digits ⋮ Banach spaces and Banach lattices of singular functions ⋮ Fractal and Hausdorff dimensions for systems of iterative functional equations

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• What's the Difference between Cantor Sets?
• A Characterization of the Nondifferentiability Set of the Cantor Function
• Dini Derivatives of Continuous Functions
• The derivative of Minkowski's \(?(x)\) function

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