  We 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.

Classical Analysis and ODEs