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The Hausdorff dimension of the level sets of Takagi’s function

Authors:	E de Amo I Bhouri

Institution:	^a Departamento de Álgebra y Análisis Matemático, Universidad de Almería, Carretera de Sacramento s/n, 04120 La Cañada de san Urbano, Almería, Spain ^b Département de Matématiques, Université de Monastir, 5000 Monastir, Tunisia ^c Departamento de Análisis Matemático, Universidad de Granada, Campus de Fuentenueva s/n, 18071 Granada, Spain ^d Grupo de Investigación de Análisis Matemático, Universidad de Almería, Carretera de Sacramento s/n, 04120 La Cañada de san Urbano, Almería, Spain

Abstract:	Recently, Maddock (2006) 12] has conjectured that the Hausdorff dimension of each level set of Takagi’s function is at most 1/2. We prove this conjecture using the self-affinity of the function of Takagi and the existing relationship between the Hausdorff and box-counting dimensions.

Keywords:	26A06 26A09 26A27
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