Let $n$ be a positive integer, let $U\subset\mathbb R^n$ be a bounded [open set](/page/Open%20Set), and let $(u_j)_{j=1}^{\infty}$ be a sequence in $W^{1,n}(U;\mathbb R^n)$. Suppose that $u\in W^{1,n}(U;\mathbb R^n)$ and
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\begin{align*}
u_j \rightharpoonup u \quad \text{in } W^{1,n}(U;\mathbb R^n).
\end{align*}
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Write $\nabla u_j,\nabla u:U\to\mathbb R^{n\times n}$ for the [weak derivative](/page/Weak%20Derivative) matrices, viewed as a.e.-defined maps in $L^n(U;\mathbb R^{n\times n})$. Then the Jacobian determinants converge to $\det \nabla u$ in the sense of distributions on $U$: for every $\phi\in C_c^\infty(U)$,