On the existence of \(C^1\) functions with perfect level sets

DOI10.4171/ZAA/983zbMath0976.26002MaRDI QIDQ5926118

D'Aniello, Emma, Udayan B. Darji

Publication date: 6 January 2002

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/48989

zbMATH Keywords

\(C^1\) functionLebesgue measure zeroperfect level set

Mathematics Subject Classification ID

Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Singular functions, Cantor functions, functions with other special properties (26A30)

Related Items (2)

\(C^n\) functions, Hausdorff measures, and analytic sets ⋮ Level sets of Hölder functions and Hausdorff measures.

Cites Work

• The Level Structure of a Residual Set of Continuous Functions
• Level sets of a typical 𝐶ⁿ function

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