Differentiability a.e. and approximate differentiability a.e

Bruckner, A. M.

doi:10.1090/S0002-9939-1977-0453938-0

Differentiability a.e. and approximate differentiability a.e
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by A. M. Bruckner PDF

Proc. Amer. Math. Soc. 66 (1977), 294-298 Request permission

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 $F|P$ is continuous.

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