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De Finetti's theorem says that an exchangeable sequence of random variables $X_i$ is a mixture of i.i.d. random variables. In other words, if $\mu$ is a measure on $\mathbb{R}^\infty$ that is ...

Let $(X_i,Y_i)_{i\in\mathbb{Z}}$ be a finite-valued stationary process whose $\sigma$-algebra of tail events is trivial. Let $\mathcal{F}_n^m$ be the $\sigma$-algebra generated by $X_n,\dots,X_m$ ($n,...