Convergence of Conze-Lesigne averages
Résumé
We study the convergence of N-1 Sigmaf(1)(T(a1n)x)f(2)(T(a2n)x)f(3)(T(a3n)x), for a measure-preserving system (X, B, mu, T) and f(1), f(2), f(3) is an element of L(infinity)(mu). This generalizes the theorem of Conze and Lesigne on such expressions and simplifies the proof. We also obtain a description of the limit.