Abstract
We give an example of a Gaussian Z 2 {\mathbb {Z}^2} -action Φ \Phi with zero entropy which is weakly mixing, rigid and such that every non-trivial measure-preserving transformation Φ g {\Phi ^g} defined by Φ , g ∈ Z 2 \Phi , g \in {\mathbb {Z}^2} , is a Bernoulli shift with infinite entropy.
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