From combinatorics to ergodic theory and back again
نویسنده
چکیده
Multiple ergodic averages, such as the average of expressions like f1(T x) f2(T x) . . . fk(T x), were first studied in the ergodic theoretic proof of Szemerédi’s Theorem on arithmetic progressions. It turns out that all constraints on such averages (in a sense that we describe) have an algebraic character, arising from identities in nilpotent groups. We discuss these averages, several generalizations, and combinatorial implications of the results. Mathematics Subject Classification (2000). 37A30, 11B25, 37A45
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تاریخ انتشار 2006