  We consider a sequence of Markov processes $\lbrace X_t^n \mid n \in
\mathbb{N} \rbrace$ with Dirichlet forms converging in the Mosco sense of Kuwae
and Shioya to the Dirichlet form associated with a Markov process $X_t$. Under
this assumption, we demonstrate that for any natural number $k$, the sequence
of Dirichlet forms corresponding to the Markov processes generated by $k$
independent copies of $\lbrace X_t^n \mid n \in \mathbb{N} \rbrace$ also
converges. As expected, the limit of this convergence is the Dirichlet form
associated with $k$ independent copies of the process $X_t$. We provide
applications of this result in the context of interacting particle systems with
Markov moment duality.
