A Pointwise Cubic Average for Two Commuting Transformations
نویسندگان
چکیده
Huang, Shao and Ye recently studied pointwise multiple averages by using suitable topological models. Using a notion of dynamical cubes introduced by the authors, the Huang-Shao-Ye technique and the Host machinery of magic systems, we prove that for a system (X, μ, S ,T ) with commuting transformations S and T , the average 1 N2 N−1 ∑ i, j=0 f0(S ix) f1(T jx) f2(S iT jx) converges a.e. as N goes to infinity for any f0, f1, f2 ∈ L∞(μ).
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