  We prove a functional central limit theorem for integrals $\int_W f(X(t))\,
dt$, where $(X(t))_{t\in\mathbb{R}^d}$ is a stationary mixing random field and
the stochastic process is indexed by the function $f$, as the integration
domain $W$ grows in Van Hove-sense. We discuss properties of the covariance
function of the asymptotic Gaussian process.
