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Dynamical systems on measure spaces, invariant measures, ergodic averages, mixing properties.

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Almost periodic functions in Tao's ergodic proof of Szemerédi's theorem

Do we say that a function $f$ is uniformly almost periodic in the aforementioned proof if $f$ is bounded (in the sense that $||f||_{L^\infty}\leq 1$) and that there exists a natural number $d>0$ such …