Invariant random subgroups of $C^*$-simple groups

RESUMO

Let $\Gamma$ be a countable discrete $C^*$-simple group. Let $\mu$ be a $\Gamma$-invariant Borel probability measure on $\text{Sub}(\Gamma)$, i.e., an IRS. We show that $\mu$-almost every subgroup $H$ is $C^*$-simple.