  In the current note we consider matrix-sequences $\{B_{n,t}\}_n$ of
increasing sizes depending on $n$ and equipped with a parameter $t>0$. For
every fixed $t>0$, we assume that each $\{B_{n,t}\}_n$ possesses a canonical
spectral/singular values symbol $f_t$ defined on $D_t\subset \R^{d}$ of finite
measure, $d\ge 1$. Furthermore, we assume that $ \{ \{ B_{n,t}\} : \, t > 0 \}
$ is an approximating class of sequences (a.c.s.) for $ \{ A_n \} $ and that $
\bigcup_{t > 0} D_t = D $ with $ D_{t + 1} \supset D_t $. Under such
assumptions and via the notion of a.c.s, we prove results on the canonical
distributions of $ \{ A_n \} $, whose symbol, when it exists, can be defined on
the, possibly unbounded, domain $D$ of finite or even infinite measure.
  We then extend the concept of a.c.s. to the case where the approximating
sequence $ \{ B_{n,t}\}_n $ has possibly a different dimension than the one of
$ \{ A_n\} $. This concept seems to be particularly natural when dealing, e.g.,
with the approximation both of a partial differential equation (PDE) and of its
(possibly unbounded, or moving) domain $D$, using an exhausting sequence of
domains $\{ D_t \}$.
  Examples coming from approximated PDEs/FDEs with either moving or unbounded
domains are presented in connection with the classical and the new notion of
a.c.s., while numerical tests and a list of open questions conclude the present
work.
