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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Differentiability through change of variables


Authors: A. M. Bruckner and C. Goffman
Journal: Proc. Amer. Math. Soc. 61 (1976), 235-241
MSC: Primary 26A24
DOI: https://doi.org/10.1090/S0002-9939-1976-0432831-2
MathSciNet review: 0432831
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Abstract: A real function $ f$ on $ [0,\;1]$ can be transformed by a homeomorphism into a differentiable function with bounded derivative if and only if $ f$ is continuous and of bounded variation. This condition does not suffice for $ f$ to be transformed into a continuously differentiable function. The additional condition for this to hold is found and the theorem is proved.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0432831-2
Keywords: Homeomorphism, differentiable function, bounded variation, variable monotonicity
Article copyright: © Copyright 1976 American Mathematical Society

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