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A counterexample on multiple convergence without commutativity

Year: 2025
Type: article
Abstract: It is shown that there exists a probability space ( X , X , μ ) (X,{\mathcal X},\mu ) , two ergodic measure preserving transformations T , S T,S acting on ( X , X , μ ) (X,{\mathcal X},\mu ) with h μ ( X , T ) = h μ ( X , S ) = 0 h_\mu (X,T)=h_\mu (X,S)=0 , and f , g ∈ L ∞ ( X , μ ) f, g \in L^\infty (X,\mu ) such that the limit lim N → ∞ 1 N ∑ n = 0 N − 1 f ( T n x ) g ( S n
Language: English
Open Access status: green
OpenAlex ID: W4415294530
FWCI: 1.608
Cites: 19
Cited by: 1
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