Nowhere-monotone differentiable functions and set of monstrous shift

DOI10.1016/j.jmaa.2023.127176zbMath1523.26003OpenAlexW4323030937MaRDI QIDQ6044187

Cheng-Han Pan

Publication date: 17 May 2023

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.2023.127176

zbMATH Keywords

Lebesgue measureBaire categorydifferentiable monsterPompeiu derivativenowhere-monotone differentiable functionPompeiu-like function

Mathematics Subject Classification ID

Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (26A27) Classification of real functions; Baire classification of sets and functions (26A21)

Cites Work

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• Some new simple proofs of old difficult theorems
• Nowhere-monotone differentiable functions and bounded variation
• An Elementary Proof of the One-Dimensional Density Theorem
• Differentiation of Real Functions
• A Short Proof of Lebesgue's Density Theorem
• Differentiability versus continuity: Restriction and extension theorems and monstrous examples
• Monsters in Calculus
• An Alternative Proof of Steinhaus’s Theorem

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