群作用的测度可扩性  

Measure-expansivity for group actions

作　　者：金秋实 董美花[1] JIN Qiushi;DONG Meihua(College of Science,Yanbian University,Yanji 133002,China)

机构地区：[1]延边大学理学院,吉林延吉133002

出　　处：《南昌大学学报（理科版）》2023年第4期307-311,共5页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(12201541);吉林省教育厅科学技术研究规划项目(612021001).

摘　　要：将可扩测度和N-可扩测度的概念推广到紧致度量空间上的群作用,并证明一个群作用是可数可扩当且仅当其是测度可扩.此外还证明了紧致度量空间上的群作用是N-可扩当且仅当每一个Borel概率测度是N-可扩.以上是现有的结论的群作用版本;如果Borel测度μ1,…,μn的凸组合是1-可扩的,则对于每一个i=1,…,n,μi是1-可扩的.最后本文将具有连续作用的1-可扩测度描述为在可扩点上支持的有限多个Dirac测度的凸和.The paper extended the concepts of expansive measures and N-expansive measures to group actions on compact metric spaces and proved that a group action is countably-expansive if and only if it is measure-expansive.It was shown that a group action of a compact metric space is N-expansive if and only if every Borel probability measure is N-expansive.These represented a group action version of the existing results.If the convex combination of Borel measuresμ1,…,μn is 1-expansive,thenμi is 1-expansive for every i=1,…,n.Finally the 1-expansive measures for continuous action was characterized as the convex sum of finitely many Dirac measures supported on expansive points.

关 键 词：测度可扩性 N-可扩测度 Borel概率测度 

分 类 号：O192[理学—数学]