On differentiability properties of typical continuous functions and Haar null sets

DOI10.1090/S0002-9939-05-08203-1zbMath1089.26003OpenAlexW1707317254MaRDI QIDQ3372091

Luděk Zajíček

Publication date: 17 February 2006

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-05-08203-1

zbMATH Keywords

approximate derivativeHaar null settypical continuous functionsnowhere differentiable functionpreponderant derivative

Mathematics Subject Classification ID

Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (26A27)

Related Items (6)

Typical martingale diverges at a typical point ⋮ On Haar meager sets ⋮ Haar null sets without \(G_{\delta}\) hulls ⋮ Haar ambivalent sets in the space of continuous functions ⋮ Haar null and Haar meager sets: a survey and new results ⋮ Properties of generic and almost every mappings in \(\mathbb Z^{\mathbb Z}\)

Cites Work

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• On Fréchet differentiability of Lipschitz maps between Banach spaces
• Porous sets that are Haar null, and nowhere approximately differentiable functions
• Some Dual Statements Concerning Wiener Measure and Baire Category
• Examples of non-shy sets
• The Prevalence of Continuous Nowhere Differentiable Functions
• Über die Differenzierbarkeit stetiger Funktionen
• Differentiability properties of typical continuous functions

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