Invariant measures on topological groups

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• 作者：Shu-Qi Huang ; ^{hshq0423@126.com" class="auth_mail" title="E-mail the corresponding author} ; Wei-Xue Shi ; ^{wxshi@nju.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：54H11 ; 28A12 ; 43A05
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：1 April 2016
• 年：2016
• 卷：202
• 期：Complete
• 页码：418-427
• 全文大小：313 K

文摘

In this paper, we prove that every locally 03a7a3696dbe24c5e0aca3" title="Click to view the MathML source">K$\mathcal{K}$ (see Definition 3.4) topological group has a nonzero outer regular invariant Borel measure when 03a7a3696dbe24c5e0aca3" title="Click to view the MathML source">K$\mathcal{K}$ is an admissible invariant family which is separated by N_G${\mathcal{N}}_G$. In this case, every open set and every member of S(K₀)$\mathcal{S}({\mathcal{K}}_0)$ are 03a7a3696dbe24c5e0aca3" title="Click to view the MathML source">K$\mathcal{K}$-inner regular. This extends the existence theorem of Haar measure on locally compact Hausdorff groups.