  In this paper we will consider the concept of $\mathbb{P}$-weakly hyperbolic
iterated function systems on compact metric spaces that generalizes the concept
of weakly hyperbolic iterated function systems, as defined by Edalat in
\cite{E} and by Arbieto, Santiago and Junqueira in \cite{ASJ} for a more
general setting where the parameter space is a compact metric space. We prove
the existence and uniqueness of the invariant measure of a $\mathbb{P}$-weakly
hyperbolic IFS. Furthermore, we prove an ergodic theorem for
$\mathbb{P}$-weakly hyperbolic IFS with compact parameter space.
