Understanding a definition from a French paper

Question

I want to understand a very special case of the following situation. The following is from the paper "Simplicité de spectres de Lyapunov et propriété d'isolation spectrale pour une famille d'opérateurs de transfert sur l'espace projectif" by Y. Guivarc'h and Emile Le Page.

Then, they go on to define Markovian System and extended Markovian systems which appear in Definition 2.6 and Definition 5.1 which go as follows.

I want to understand what happens to $Q_x$ when $X$ is a single point. Does it become equal to $\mu^{\mathbb{N}}$ if $q_n(x,\omega)=1$ for all $n$?

Thank you for the help!