Point process theory: Proof that strong mixing implies mixing.

Question

Here's the problem: I'm working on a paper that says that strong mixing condition for stationary point processes implies the process to be mixing, but it never proves it (the paper is Ivanoff, Central limit theorem for point processes). Here's the two definitions: Mixing: Let $T_t$ be the operator defined on the point process $\Phi$ as $T_t\Phi(A)=\Phi(A+t)$ $\forall A\in\mathcal{B}_{\mathbb{R}^d}$, then the point process $\Phi$ with distribution Q is mixing if $Q(U\cap T_t(V))\xrightarrow{t\rightarrow\infty}Q(U)Q(V)$ for $U,V\in\mathscr{N}^*$ the sigma algebra in the space of point processes. Strong mixing:Let $\Phi$ be a stationary point process, and $\mathscr{F}(A)$ the sigma algebra generated by the random variables $\Phi(A')$, $A'\subset A$, $A\in\mathcal{B}_{\mathbb{R}^d}$. Let $\bar{\alpha}=sup[\alpha(\mathscr{F}(A),\mathscr{F}(B)):\rho(A,B)\geq r,d(A)\leq l,d(B)\leq l]$, where $\rho(A,B)$ is the distance between A and B and $d(A)$ is the diameter of A and $\alpha(\mathscr{F}(A),\mathscr{F}(B))$=$sup[\mid\mathbb{P}(U)\mathbb{P}(V)-\mathbb{P}(U\cap V)\mid$:$U\in\mathscr{F}(A),V\in\mathscr{F}(B)]$. $\Phi$ is said to be strong mixing if $\alpha(kr,kl)\xrightarrow{k\rightarrow\infty}0$. I hope it's clear enough to understand the question, I didn't define everything, you should have a minimum of knowledge of stochastic geometry to help me with this. Thank you in advanced!