Random subgroup

Definition
Suppose $$G$$ is a locally compact group. Denote by $$\mathcal{C}(G)$$ the collection of closed subgroups of $$G$$, equipped with the defining ingredient::Chabauty topology.

A random subgroup (IRS) on $$G$$ is a probability measure on the set $$\mathcal{C}(G)$$ satisfying the following condition: It is a Borel measure with respect to the Chabauty topology, i.e., all Borel subsets under the Chabauty topology are measurable.