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Dynamical systems on measure spaces, invariant measures, ergodic averages, mixing properties.
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Ergodicity of composition with a rotation
Let $T$ be an arbitrary Lebesgue measure-preserving automorphism of the unit interval $I$. Let $R_{\alpha}$ denote rotation by $\alpha$, i.e. $R_{\alpha}(x)=x+\alpha \pmod{1}$ for $x \in I$ and $\alp …