  It is shown that $u_k \cdot v_k$ converges weakly to $u\cdot v$ if
$u_k\weakto u$ weakly in $L^p$ and $v_k\weakly v$ weakly in $L^q$ with $p, q\in
(1,\infty)$, $1/p+1/q=1$, under the additional assumptions that the sequences
$\Div u_k$ and $\curl v_k$ are compact in the dual space of $W^{1,\infty}_0$
and that $u_k\cdot v_k$ is equi-integrable. The main point is that we only
require equi-integrability of the scalar product $u_k\cdot v_k$ and not of the
individual sequences.
