Given a process $X_n \xrightarrow{d} X$ on some probability space $(\Omega,\mathcal{A},P)$. If for every $B \in \mathcal{A}$ it holds, that $$ \lim_{n\rightarrow \infty} P(X_n\in A,B)=P(X\in A)P(B) $$ and any set $A$ of continuity of the distribution function of $X$, we say the convergence is renyi-mixing in the classical discrete time sense. This is shown to be equivalent to: Fix $m$ and for $B\in \sigma(X_{1},\ldots,X_{m})$ with $P(B)>0$ then $$ \lim_{n\rightarrow \infty} P(X_n\in A|B)=P(X\in A) $$
Now lets say we have a continuous time proces $X_t$ with $X_t\xrightarrow{d}X$. If we want the convergence to be renyi-mixing, is it sufficient to show, that for any countable grid $(t_i)_{i\in\mathbb{N}}$ with $t_{i}\rightarrow \infty$ as $i\rightarrow \infty$ $$ \lim_{i\rightarrow \infty}P(X_{t_i}\in A,B)=P(X\in A)P(B) $$ holds?
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