Let $U\subset\mathbb R^n$ be open, and let $f:U\times\mathbb R\times\mathbb R^n\to(-\infty,\infty]$ be a Caratheodory integrand, meaning that for every $(s,\xi)\in\mathbb R\times\mathbb R^n$ the section $x\mapsto f(x,s,\xi)$ is Lebesgue measurable on $U$, and there exists a set $N\subset U$ with $\mathcal L^n(N)=0$ such that for every $x\in U\setminus N$ the map $(s,\xi)\mapsto f(x,s,\xi)$ is continuous from $\mathbb R\times\mathbb R^n$ into $(-\infty,\infty]$ with the extended-real topology. If $u:U\to\mathbb R$ and $v:U\to\mathbb R^n$ are Lebesgue measurable maps, then the map

\begin{align*} U&\to(-\infty,\infty],\qquad x\mapsto f(x,u(x),v(x)) \end{align*}

is Lebesgue measurable.