Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial Averages Converge to the Product of Integrals   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 categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: solv-int