Abstract
Extending Malý's geometric definition of absolutely continuous functions of $n$ variables (in a sense equivalent to that of Rado-Reichelderfer), we define classes of $p$-absolutely continuous functions $(1\leq p \lt n)$ and show that this weaker notion of absolute continuity still implies differentiability almost everywhere, although it does not imply continuity or Lusin's condition (N).
Citation
Donatella Bongiorno. "A regularity condition in Sobolev spaces $W^{1,p}_{\mathrm loc}({\mathbb R}^n)$ with $1 ≤ p \lt n$." Illinois J. Math. 46 (2) 557 - 570, Summer 2002. https://doi.org/10.1215/ijm/1258136211
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