Ergodic theorems for the shift action and pointwise versions of the Abért-Weiss theorem

被引：0
作者：
Anton Bernshteyn
机构：
[1] University of Illinois at Urbana–Champaign,Department of Mathematics
[2] Carnegie Mellon University,Department of Mathematical Sciences
来源：
Israel Journal of Mathematics | 2020年 / 235卷
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摘要：
Let Γ be a countably infinite group. A common theme in ergodic theory is to start with a probability measure-preserving (p.m.p.) action Γ ↷ (X, μ) and a map f ∈ L1 (X, μ), and to compare the global average ∫ f dμ of f to the pointwise averages ∣D∣−1 ∑δ∈Df(δ · x), where x ∈ X and D is a nonempty finite subset of Γ. The basic hope is that, when D runs over a suitably chosen infinite sequence, these pointwise averages should converge to the global value for μ-almost all x.
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页码：255 / 293
页数：38
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