2022-08-09T02:43:57Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000040312021-03-01T19:47:58Z離散群のストーン－チェック境界と測度同値理論Stone-Čech boundaries of discrete groups and measure equivalence theorySAKO, Hiroki9306410University of Tokyo (東京大学)博士(数理科学)We get three types of results on measure equivalence theory: directproduct groups of Ozawa's class S groups, wreath product groups and amalgamatedfree products. We prove measure equivalence factorization results on directproduct groups of Ozawa's class S groups. As consequences, Monod-Shalom typeorbit equivalence rigidity theorems follow. We prove that if two wreath productgroups A≀G, B≀Γ of non-amenable exact direct product groups G, Γ with amenablebases A, B are measure equivalent, then G and Γ are measure equivalent. Rigidityresults on amalgamated free products of non-amenable exact direct productgroups are also shown. We also prove that being in Ozawa's class S of countablediscrete groups is invariant under measure equivalence.thesis2010-03-242010-03-24application/pdfapplication/pdf甲第26108号https://repository.dl.itc.u-tokyo.ac.jp/record/4031/files/SakoH_22_3_PhD_a.pdfhttps://repository.dl.itc.u-tokyo.ac.jp/record/4031/files/SakoH_22_3_PhD_b.pdfeng