On continuous functions with no unilateral derivatives
Annales de l'Institut Fourier, Tome 38 (1988) no. 2, p. 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.
@article{AIF_1988__38_2_43_0,
     author = {Hata, Masayoshi},
     title = {On continuous functions with no unilateral derivatives},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {38},
     number = {2},
     year = {1988},
     pages = {43-62},
     doi = {10.5802/aif.1134},
     zbl = {0641.26010},
     mrnumber = {89i:26006},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1988__38_2_43_0}
}
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. http://www.numdam.org/item/AIF_1988__38_2_43_0/

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