Random subgroup

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Definition

Suppose G is a locally compact group. Denote by \mathcal{C}(G) the collection of closed subgroups of G, equipped with the 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.