乘积和linear orders空间上的不变测度
Invariant measures on products and on the space of linear orders
摘要：
设$M$是一个$\aleph_0$ -范畴结构，并假定$M$不具有代数性和弱消元.推广了de Finetti和Ryll-Nardzewski的经典定理，证明了$[0, 1]^M$上的任何遍历的、$\operatorname{Aut}(M)$ -不变测度都是乘积测度.我们还研究了$\operatorname{Aut}(M)$在$M$上的线性阶紧空间$\mathrm{LO}(M)$上的作用.如果我们进一步假设作用$\operatorname{Aut}(M) \curvearrowright M$是传递的，我们证明了作用$\operatorname{Aut}(M) \curvearrowright \mathrm{LO}(M)$或者有一个不动点或者是唯一遍历的。
英文摘要：
Let $M$ be an $\aleph_0$-categorical structure and assume that $M$ has no algebraicity and has weak elimination of imaginaries. Generalizing classical theorems of de Finetti and Ryll-Nardzewski, we show that any ergodic, $\operatorname{Aut}(M)$-invariant measure on $[0, 1]^M$ is a product measure. We also investigate the action of $\operatorname{Aut}(M)$ on the compact space $\mathrm{LO}(M)$ of linear orders on $M$. If we assume moreover that the action $\operatorname{Aut}(M) \curvearrowright M$ is transitive, we prove that the action $\operatorname{Aut}(M) \curvearrowright \mathrm{LO}(M)$ either has a fixed point or is uniquely ergodic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
