2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62792We extend Federer's coarea formula to mappings $f$ belonging to the Sobolev class $W^{1,p}(R^n;R^m)$, $1 \le m < n$, $p>m$, and more generally, to mappings with gradient in the Lorentz space $L^{m,1}(R^n)$. This is accomplished by showing that the graph of $f$ in $R^{n+m}$ is a Hausdorff $n$-rectifiable set.Submitted for publication, 16 pagesClassical Analysis and ODEs46E35, 46E30text