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On continuous functions with no unilateral derivatives

Masayoshi Hata — 1988

Annales de l'institut Fourier

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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