Let $n\ge 1$, let $(M,\omega)$ be a symplectic manifold of dimension $2n$, and let $\Sigma\subset M$ be an embedded hypersurface. Suppose that $Y\in\mathfrak X(U)$ is a Liouville vector field on an open neighbourhood $U\subset M$ of $\Sigma$, transverse to $\Sigma$, so that