Definition 1

— Let $\mathscr{T} = (T_i, p_{ij})$ be an inverse system of topological spaces indexed by I. One calls inverse system (resp. sub-inverse system) of measures on $\mathscr{T}$ a family $(\mu_i)_{i \in I}$, where $\mu_i$ is a bounded measure on $T_i$ for all $i \in I$, and where $\mu_i = p_{ij}(\mu_j)$ (resp. $\mu_i \geq p_{ij}(\mu_j)$) for $i \leq j$.