Density of discrete semigroup flows

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• 作者：Prachi Loliencar ^{lolienca@ualberta.ca}
• 关键词：Abstract harmonic analysis ; Transformation semigroup ; Flow ; Stone&ndash ; Čech compactification ; F&oslash ; lner condition ; Amenability
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 April 2017
• 年：2017
• 卷：448
• 期：1
• 页码：633-649
• 全文大小：415 K
• 卷排序：448

文摘

We generalize the notions of upper and lower density on semigroups to semigroup flows. We then show that when the Strong Følner Condition holds, there exist upper densities on the flow satisfying classical properties such as partition regularity of positive sets, finite additivity on translates, and invariance under semigroup action. We also introduce the concept of Følner density of a flow and show that under a certain condition, it is multiplicative on products.