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Wednesday, September 11, 2019

**Abstract:** Given a Borel measure-preserving action of a Polish group $G$ on $\left[ 0,1 \right]$, ignoring null sets gives a corresponding action on the measure algebra. If $G$ is locally compact, this can always be reversed: a measure-preserving action on the measure algebra of $\left[ 0,1 \right]$ can always be induced by a (pointwise) action on $\left[ 0,1 \right]$. This fails in the non-locally-compact case. In this talk, I will discuss a dynamical condition on the action ("whirliness") which characterizes when an action on the measure algebra admits a pointwise realization. This talk is based on 'Spatial and non-spatial actions of Polish groups' by E Glasner and B Weiss.