کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8896669 | 1630594 | 2018 | 27 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The space of stable weak equivalence classes of measure-preserving actions
ترجمه فارسی عنوان
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
The concept of (stable) weak containment for measure-preserving actions of a countable group Î is analogous to the classical notion of (stable) weak containment of unitary representations. If Î is amenable then the Rokhlin lemma shows that all essentially free actions are weakly equivalent. However if Î is non-amenable then there can be many different weak and stable weak equivalence classes. Our main result is that the set of stable weak equivalence classes naturally admits the structure of a Choquet simplex. For example, when Î=Z this simplex has only a countable set of extreme points but when Î is a nonamenable free group, this simplex is the Poulsen simplex. We also show that when Î contains a nonabelian free group, this simplex has uncountably many strongly ergodic essentially free extreme points.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 274, Issue 11, 1 June 2018, Pages 3170-3196
Journal: Journal of Functional Analysis - Volume 274, Issue 11, 1 June 2018, Pages 3170-3196
نویسندگان
Lewis Bowen, Robin Tucker-Drob,