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A measure-preserving system is a probability space $(X,\mathcal B,\mu)$ with a measurable map $T\colon X\to X$ preserving the measure, that is $\mu(T^{—1}A)=\mu(A)$ for all $A$ measurable.

We can study these objects for example working on weakly-stationnary processes, as they can be represented by $X_i=f\circ T^i$ where $f$ is some measurable map.

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