论文标题
产品和线性订单空间的不变措施
Invariant measures on products and on the space of linear orders
论文作者
论文摘要
令$ m $为$ \ aleph_0 $ - 分类结构，并假设$ m $没有代数，并且消除了想象力。概括了de Finetti和Ryll-Nardzewski的经典定理，我们表明，任何Ergodic，$ \ permatatorname {aut}（m）$ - $ [0，1]^m $不变的度量是产品度量。我们还调查了紧凑型空间$ \ mathrm {lo}（m）$ $ m $上的$ \ operatotorName {aut}（m）$在$ m $上的行动。如果我们假设动作$ \ operatorAtorname {aut}（m）\ curvearrowright m $是传递的，我们证明了动作$ \ operatotorname {aut}（aut}（m）\ curvearrowright \ mathrm {lo}（mathrm {lo}（m），或者是固定点，或者是固定点或独特的磨性。
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.
