A functional central limit theorem for integrals of stationary mixing random fields

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We prove a functional central limit theorem for integrals ∫W f(X(t)) dt, where (X(t))tᵈ 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.