The invariance principle for stationary random fields satisfying the strong mixing condition

Let $\xi(u)$, $u\in R^q$, be a stationary random field satisfying the strong mixing condition, $V$ be an open set in $R^q$ with finite Lebesgue's measure $\mu(V)$,
$$ T(V)=\int_V\xi(u)\,du, $$
The sufficient condition for the weak convergence of
$$ \zeta_r(t)=(r^q\mu(V))^{-1/2}T(rt^{1/q}V),\qquad t\in[0,1], $$
to some Gaussian process $w_V(t)$ are obtained.