Jacobians of BV homeomorphisms and their weak-* limits

Abstract: We prove that in $\mathbb{R}<sup>3$ any $BV$ homeomorphism as well as the weak-* limit of $BV$ homeomorphisms cannot change the sign of the Jacobian, i.e., we have $J_f \geq 0$ almost everywhere or $J_f \leq 0$ almost everywhere.