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Transactions of the American Mathematical Society

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Where the continuous functions without unilateral derivatives are typical


Author: Jan Malý
Journal: Trans. Amer. Math. Soc. 283 (1984), 169-175
MSC: Primary 26A27
DOI: https://doi.org/10.1090/S0002-9947-1984-0735414-9
MathSciNet review: 735414
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Abstract: An alternative proof of the existence of a Besicovitch function (i.e. a continuous function which has nowhere a unilateral derivative) is presented. The method consists in showing the residuality of Besicovitch functions in special subspaces of the Banach space of all continuous functions on $ [0,1]$ and yields Besicovitch functions with additional properties of Morse or Hölder type. A way how to obtain functions with a similar behavior on normed linear spaces is briefly mentioned.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1984-0735414-9
Keywords: Besicovitch function, unilateral derivative, residual sets in function spaces
Article copyright: © Copyright 1984 American Mathematical Society

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