Note on Lusin $(N)$ condition and the distributional determinant

Abstract

Let $\Omega\subset\rn$ be an open set. We show that for a continuous mapping $f\in W^{1,n-1}(\Omega,\rn)$ with $J_f\in L^1(\Omega)$ the validity of the Lusin $(N)$ condition implies that the distributional Jacobian equals to the pointwise Jacobian.

Keywords

• Jacobian
• distributional Jacobian