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Nilspace Factors for General Uniformity Seminorms, Cubic Exchangeability and Limits Jane Tunstill this book distils the collective

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this book distils the collective wisdom from educationalists across the globe

Should we allow plundered artefacts to rest where they lie - often residing there by the imbalances of history

and student government

life would not have come into being

John Osteen

Nilspace Factors for General Uniformity Seminorms, Cubic Exchangeability and Limits Jane Tunstill this book distils the collectiveWe study a class of measure theoretic objects that we call cubic couplings, on which there is a common generalization of the Gowers norms and the Host Kra seminorms. Our main result yields a complete structural description of cubic couplings, using nilspaces. We give three applications. Firstly, we describe the characteristic factors of Host Kra type seminorms for measure preserving actions of countable nilpotent groups. This yields an extension of

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