no. 2
On continuous functions with no unilateral derivatives
Annales de l'Institut Fourier, Tome 38 (1988) no. 2, pp. 43-62.

On construit une famille de fonctions continues sur l’intervalle [0,1] qui n’a nulle part de dérivée unilatérale finie ou infinie utilisant les équations fonctionnelles de De Rham. Puis on démontre que, pour tout α∈[0,1), il existe une f α dans toute classe lipschitzienne d’ordre inférieur à 1 tel que la mesure de l’ensemble de nœud points de f α est égale à α.

We construct a family of continuous functions on the unit interval which have nowhere a unilateral derivative finite or infinite by using De Rham’s functional equations. Then we show that for any α ∈[0,1) there exists an f α in any Lipschitz class of order less than one such that the set of knot points of f α has a measure α.

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     author = {Hata, Masayoshi},
     title = {On continuous functions with no unilateral derivatives},
     journal = {Annales de l'Institut Fourier},
     pages = {43--62},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {38},
     number = {2},
     year = {1988},
     doi = {10.5802/aif.1134},
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     mrnumber = {89i:26006},
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Hata, Masayoshi. On continuous functions with no unilateral derivatives. Annales de l'Institut Fourier, Tome 38 (1988) no. 2, pp. 43-62. doi : 10.5802/aif.1134. https://aif.centre-mersenne.org/articles/10.5802/aif.1134/

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