A remarks on absolutely continuous functions in \(\mathbb R_n\) (Q997538)

The authors introduce a notion of absolute continuity, namely \(\alpha,\lambda\)-absolute continuity, for functions defined in an open set of \(\mathbb R^n\) and taking values in \(\mathbb R^m\). An \(\alpha,\lambda\)-absolute continuous function is also absolute continuous in the sense of Hencl. The authors prove that \(\alpha,\lambda\)-absolute continuity implies continuity, weak differentiability, differentiability almost everywhere, area and coarea formulas. An example of a function which is absolutely continuous in Hencl's sense, but not in the sense introduced in the paper is given in the last section.