Every countably infinite group is almost Ornstein

We say that a countable discrete group $G$ is {\em almost Ornstein} if for every pair of standard non-two-atom probability spaces $(K,κ), (L,λ)$ with the same Shannon entropy, the Bernoulli shifts $G \cc (K^G,κ^G)$ and $G \cc (L^G,λ^G)$ are isomorphic.

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