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Two ergodic probability measure-preserving systems in ergodic theory, $T$ of $(X,\mu)$ and $S$ of $(Y,\nu)$, are said to be disjoint if the only joining (i.e. $T\times S$-invariant measure on $X\times …

Here is a lemma that I know to be true, and can prove in half a page or so, but I'm wondering: can anyone supply a reference so that it can simply be quoted in a paper? Lemma Let $T$ be an ergodic …

One version of Oseledets' Multiplicative Ergodic Theorem states that if $\sigma$ is an ergodic measure-preserving transformation of a space $(\Omega,\mathbb P)$ and if $A\colon\Omega\to GL(d,\mathbb R …

A useful "abstract nonsense" construction in ergodic theory takes a measure-preserving transformation $T$ of a probability space $(X,\mathcal B,\mu)$ and extends it to an invertible measure-preserving …

Hello MO World I'm working on a paper involving embedding your favourite measure-preserving transformation into a topological model (think Krieger generator theorem: embedding in a full shift) and ha …

Dear MO_World, I have (another) question about relaxing the assumptions in the sub-additive ergodic theorem. Apologies if this is something I should know already... There are a number of statements …

I've been working on a problem I'm working on in ergodic theory (finding Alpern lemmas for measure-preserving $\mathbb R^d$ actions) and have found some neat tilings, that I presume were previously kn …

Can anyone help me out with proofs/counterexamples? I'm working on an operator-valued multiplicative ergodic theorem and need what may(?) be a well-known fact. This fact (if true) would help me get ri …

I'm hoping for some ideas/pointers here. I'm experimenting with a Livschitz theorem for functions on a locally compact Abelian group, where the periodic orbit sums take values in a closed subgroup. …