A classification of orbits admitting a unique invariant measure

被引：3

作者：

Ackerman, Nathanael ^{[1
]}

Freer, Cameron ^{[2
]}

Kwiatkowska, Aleksandra ^{[3
,4
]}

Patel, Rehana ^{[5
]}

机构：

[1] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

[2] MIT, Dept Brain & Cognit Sci, E25-618, Cambridge, MA 02139 USA

[3] Univ Bonn, Math Inst, Endenicher Allee 60, D-53115 Bonn, Germany

[4] Uniwersytet Wroclawski, Inst Matemat, Pl Grunwaldzki 2-4, PL-50384 Wroclaw, Poland

[5] Franklin W Olin Coll Engn, Needham, MA 02492 USA

来源：

ANNALS OF PURE AND APPLIED LOGIC | 2017年 / 168卷 / 01期

关键词：

Invariant measure; High homogeneity; Unique ergodicity; GRAPHS;

D O I：

10.1016/j.apal.2016.08.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the space of countable structures with fixed underlying set in a given countable language. We show that the number of ergodic probability measures on this space that are S-infinity-invariant and concentrated on a single isomorphism class must be zero, or one, or continuum. Further, such an isomorphism class admits a unique S-infinity-invariant probability measure precisely when the structure is highly homogeneous; by a result of Peter J. Cameron, these are the structures that are interdefinable with one of the five reducts of the rational linear order (Q, <). (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：19 / 36

页数：18