# Random subgroup

From Groupprops

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## Definition

Suppose is a locally compact group. Denote by the collection of closed subgroups of , equipped with the Chabauty topology.

A **random subgroup** (**IRS**) on is a probability measure on the set 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.