Approximate invariance for ergodic actions of amenable groups.

IF 1 3区数学 Q1 MATHEMATICS Discrete Analysis Pub Date : 2016-07-01 DOI:10.19086/DA.8471

M. Bjorklund, A. Fish

引用次数: 7

Abstract

We develop in this paper some general techniques to analyze action sets of small doubling for probability measure-preserving actions of amenable groups. As an application of these techniques, we prove a dynamical generalization of Kneser's celebrated density theorem for subsets in $(\bZ,+)$, valid for any countable amenable group, and we show how it can be used to establish a plethora of new inverse product set theorems for upper and lower asymptotic densities. We provide several examples demonstrating that our results are optimal for the settings under study.

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可服从群遍历作用的近似不变性。

本文给出了分析可服从群的概率测度保持行动的小加倍行动集的一般方法。作为这些技术的一个应用，我们证明了Kneser著名的密度定理在$(\bZ，+)$中的子集的一个动态推广，它对任何可数可调群都有效，并且我们展示了如何使用它来建立大量新的关于上下渐近密度的逆积集定理。我们提供了几个例子来证明我们的结果对于所研究的设置是最佳的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Analysis Mathematics-Algebra and Number Theory

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

17 weeks

期刊介绍： Discrete Analysis is a mathematical journal that aims to publish articles that are analytical in flavour but that also have an impact on the study of discrete structures. The areas covered include (all or parts of) harmonic analysis, ergodic theory, topological dynamics, growth in groups, analytic number theory, additive combinatorics, combinatorial number theory, extremal and probabilistic combinatorics, combinatorial geometry, convexity, metric geometry, and theoretical computer science. As a rough guideline, we are looking for papers that are likely to be of genuine interest to the editors of the journal.

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