# Polynomial averages converge to the product of integrals

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DOI: 10.1007/BF02775439

- Cite this article as:
- Frantzikinakis, N. & Kra, B. Isr. J. Math. (2005) 148: 267. doi:10.1007/BF02775439

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## Abstract

We answer a question posed by Vitaly Bergelson, showing that in a totally ergodic system, the average of a product of functions evaluated along polynomial times, with polynomials of pairwise differing degrees, converges in*L*^{2} to the product of the integrals. Such averages are characterized by nilsystems and so we reduce the problem to one of uniform distribution of polynomial sequences on nilmanifolds.

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© The Hebrew University Magnes Press 2005