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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Differentiability a.e. and approximate differentiability a.e


Author: A. M. Bruckner
Journal: Proc. Amer. Math. Soc. 66 (1977), 294-298
MSC: Primary 26A24; Secondary 26A21, 26A45
MathSciNet review: 0453938
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Abstract: Let F be a finite real valued function defined on [0, 1]. We prove that F can be transformed into a function which is differentiable a.e. by a homeomorphic change of variables if and only if F is continuous on a dense set. We also show that F can be transformed into a function which is approximately differentiable a.e. if and only if each interval $ I \subset [0,1]$ contains a nonempty perfect set P such that $ F\vert P$ is continuous.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0453938-0
PII: S 0002-9939(1977)0453938-0
Keywords: Differentiability, approximate differentiability, generalized bounded variation (VBG, $ VBG_\ast$)
Article copyright: © Copyright 1977 American Mathematical Society