Note on Lusin (N) condition and the distributional determinant

Let Ω⊂RnΩ⊂Rn be an open set. We show that for a continuous mapping f∈W1,n−1(Ω,Rn)f∈W1,n−1(Ω,Rn) with Jf∈L1(Ω)Jf∈L1(Ω) the validity of the Lusin (N) condition implies that the distributional Jacobian equals to the pointwise Jacobian.