A Plünnecke–Ruzsa inequality in compact abelian groups
A Plünnecke–Ruzsa inequality in compact abelian groups
复制标题
紧阿贝尔群中的 Plünnecke-Ruzsa 不等式
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Anne de Roton
中科院分区：
文献类型：
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作者：
P. Candela;Diego González;Anne de Roton
Plunnecke-Ruzsa 不等式是控制重复加法和减法下阿贝尔群有限子集增长的基本工具。其他处理求和集的工具通过扩展到更一般组的更一般子集而获得了适用性。这促使扩展 Plüunnecke-Ruzsa 不等式，特别是通过用 Haar 概率度量替换基数来扩展紧凑交换群的可测量子集。该目标与加法下 Haar 可测集类的稳定性问题相关。在这个方向上，解析集类是很自然的工作对象。我们证明了一般紧（Hausdorff）阿贝尔群中 K 解析集的 Plunnecke-Ruzsa 不等式。我们还讨论了进一步的扩展，其中一些扩展提出了描述拓扑中独立感兴趣的问题。
The Plunnecke–Ruzsa inequality is a fundamental tool to control the growth of finite subsets of abelian groups under repeated addition and subtraction. Other tools to handle sumsets have gained applicability by being extended to more general subsets of more general groups. This motivates extending the Pl¨unnecke–Ruzsa inequality, in particular to measurable subsets of compact abelian groups by replacing the cardinality with the Haar probability measure. This objective is related to the question of the stability of classes of Haar measurable sets under addition. In this direction the class of analytic sets is a natural one to work with. We prove a Plunnecke–Ruzsa inequality for K-analytic sets in general compact (Hausdorff) abelian groups. We also discuss further extensions, some of which raise questions of independent interest in descriptive topology.