Abstract
We show that each homeomorphism $f$ in the Sobolev space $W^{1,1}_{\loc}(\Omega,\rn)$ satisfies either $J_f\geq 0$ a.e or $J_f\leq 0$ a.e. if $n=2$ or $n=3$. For $n>3$ we prove the same conclusion under stronger assumption that $f\in W^{1,s}_{\loc}(\Omega,\rn)$ for some $s>[n/2]$.