We introduce the notion of density of a rational language with respect to a sequence of probability measures. We prove that if $(\mu_n)$ is a sequence of Bernoulli measures converging to a positive Bernoulli measure $\overline{ \mu}$, the sequential density is the ordinary density with respect to $\overline{ \mu}$. We also prove that if $(\mu_n)$ is a sequence of invariant probability measures converging in the strong sense to an invariant probability measure $\overline{ \mu}$, then the sequential density of every rational language exists for this sequence.
Categories: math.DS cs.FL