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Differentiable functions which do not satisfy a uniform Lipschitz condition of any order


Author: Masayoshi Hata
Journal: Proc. Amer. Math. Soc. 111 (1991), 443-450
MSC: Primary 26A16; Secondary 26A27
DOI: https://doi.org/10.1090/S0002-9939-1991-1045138-8
MathSciNet review: 1045138
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Abstract: The aim of this paper is to construct two kinds of absolutely continuous functions. One is differentiable everywhere but does not satisfy a uniform Lipschitz condition of any order on some large class of subintervals, while the other is differentiable almost everywhere but does not satisfy a uniform Lipschitz condition of any order on any subintervals.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1045138-8
Keywords: Lipschitz conditions, discontinuous derivatives
Article copyright: © Copyright 1991 American Mathematical Society

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