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Let $G$ be an at most countable discrete group acting freely on a standard probability measure space $X$ in a measure preserving way. It is well known that if $G$ is a finite group then this action a …

The Dye Theorem states that any two free ergodic p.m.p automorphisms of a standard probability space are orbit-equivalent. Question: Is there a version of the above theorem for non-ergodic autom …

Originally posted on Maths StackExchange, but repositing here because of getting no answer there. Not a research question really - I'm just confused by implications between various ergodic theorems …

Let $M\subset B(\mathcal H)$ be a finite von Neumann algebra of bounded operators on a Hilbert space $\mathcal H$., let $P\in M$ be a self-adjoint operator with a pure-point spectrum (for example a pr …

Quick version of the question. Let $(X, \mu)$ be a probability measure space and let $Z$, the group of integers, act on $X$ in a measure preserving way. How can I decompose $X$ into ergodic compon …

In the paper "Orbit Equivalence and Topological Conjugacy of Affine Actions on Compact Abelian Groups", S. Bhattacharya shows (Theorem 3) the following: Theorem. Given two actions $\alpha$ and $\b …

This is an improved version of my previous question, where I forgot to put one of the assumptions. Question. Let $G$ be a finitely generated non-amenable discrete group, and $H$ be a subgroup of …

Question. Give a (possibly elementary) example of a probability measure preserving action $\rho\colon G \curvearrowright X$ of a finitely-generated discrete group $G$ on a standard borel space $X$ w …