### Ergodic seminorms for commuting transformations and applications

Bernard Host (2009)

Studia Mathematica

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Recently, T. Tao gave a finitary proof of a convergence theorem for multiple averages with several commuting transformations, and soon thereafter T. Austin gave an ergodic proof of the same result. Although we give here another proof of the same theorem, this is not the main goal of this paper. Our main concern is to provide tools for the case of several commuting transformations, similar to the tools successfully used in the case of a single transformation, with the idea that they may...