Geodesic
On Differentiable Functions having an Everywhere Dense set of Intervals of Constancy
Canadian mathematical bulletin, Tome 8 (1965) no. 1, pp. 73-76

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The Cantor function C [2; p. 213], which appears in analysis as a simple example of a continuous increasing function which is not absolutely continuous, has the following properties: (i) C is defined on [0,1], with C(0) = 0, C (l) = l; (ii) C is continuous and non-decreasing on [0,1]; (iii) C is constant on each interval contiguous to the perfect Cantor set P; (iv) C fails to be constant on any open interval containing points of P; (v) The set of points at which C is non-differentiable is non-denumerable. 
Bruckner, A. M.; Leonard, John L. On Differentiable Functions having an Everywhere Dense set of Intervals of Constancy. Canadian mathematical bulletin, Tome 8 (1965) no. 1, pp. 73-76. doi: 10.4153/CMB-1965-009-1
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