Real Analysis Exchange

The Hausdorff Dimension of the Generalized Level Sets of Takagi's Function

Manuel Díaz Carrillo, Juan Fernández Sánchez, and Enrique de Amo

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Abstract

In this note we prove that 1/2 is an upper bound for the Hausdorff dimension of the intersection of the graph of Takagi's function with any line of integer slope.

Article information

Source
Real Anal. Exchange, Volume 38, Number 2 (2012), 421-424.

Dates
First available in Project Euclid: 27 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.rae/1403894901

Mathematical Reviews number (MathSciNet)
MR3261886

Zentralblatt MATH identifier
1298.28014

Subjects
Primary: 26A06: One-variable calculus 26A27: Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
Secondary: 26A30: Singular functions, Cantor functions, functions with other special properties

Keywords
Hausdorff dimension box-counting dimension Takagi's function generalized level set

Citation

de Amo, Enrique; Díaz Carrillo, Manuel; Fernández Sánchez, Juan. The Hausdorff Dimension of the Generalized Level Sets of Takagi's Function. Real Anal. Exchange 38 (2012), no. 2, 421--424. https://projecteuclid.org/euclid.rae/1403894901


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