Let $U \subset \mathbb{R}^n$ be open, let $1 < p < \infty$, and let $q = p/(p-1)$ be the conjugate exponent. If $\{u_n\}_{n=1}^\infty \subset L^p(U)$ [converges weakly](/page/Weak%20Convergence) to $u \in L^p(U)$ and $\{v_n\}_{n=1}^\infty \subset L^q(U)$ converges strongly to $v \in L^q(U)$, then \begin{align*} \int_U u_n v_n \, d\mathcal{L}^n \to \int_U u v \, d\mathcal{L}^n. \end{align*}