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Given a countable essentially free ergodic non-singular group action $G \curvearrowright (X, \mu)$ on a standard measure space, suppose $\mu$ is a non-atomic probability measure and $\alpha: G \...

I hope this is an appropriate question for this forum. If not, I apologize. Before stating my question (which may be found at the end of this post), I will attempt to provide sufficient context. I ...