Pointwise convergence of certain continuous-time double ergodic averages
نویسندگان
چکیده
منابع مشابه
Pointwise Convergence of Some Multiple Ergodic Averages
We show that for every ergodic system (X, μ,T1, . . . ,Td) with commuting transformations, the average 1 Nd+1 ∑ 0≤n1,...,nd≤N−1 ∑ 0≤n≤N−1 f1(T n 1 d ∏ j=1 T n j j x) f2(T n 2 d ∏ j=1 T n j j x) · · · fd(T n d d ∏ j=1 T n j j x). converges for μ-a.e. x ∈ X as N → ∞. If X is distal, we prove that the average 1 N N ∑ i=0 f1(T n 1 x) f2(T n 2 x) · · · fd(T n d x) converges for μ-a.e. x ∈ X as N → ∞...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2021
ISSN: 0143-3857,1469-4417
DOI: 10.1017/etds.2021.45