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Zeitschrift für Analysis und ihre Anwendungen

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Volume 29, Issue 1, 2010, pp. 107–115
DOI: 10.4171/ZAA/1400

Published online: 2010-01-04

Approximate Differentiability Almost Everywhere

Emma D’Aniello[1] and Paolo de Lucia[2]

(1) Università degli Studi Federico II, Caserta, Italy
(2) Università degli Studi di Napoli Federico II, Italy

Let X be a bounded measurable subset of ℝk. We provide a characterization of the functions f : X → ℝ approximately differentiable almost everywhere. An important tool in the proof is a Saks’ Theorem-type result.

Keywords: Parameter of regularity, asymptotically differentiable function, D-differentiable function, approximately differentiable function

D’Aniello Emma, de Lucia Paolo: Approximate Differentiability Almost Everywhere. Z. Anal. Anwend. 29 (2010), 107-115. doi: 10.4171/ZAA/1400