连续遍历容量
Continuous Ergodic Capacities
摘要：
本文的目的是刻画连续遍历上概率$\mathbb{V}=\sup_{P\inΘ}P$的集合$Θ$的结构（定理\ref {主要结果}）：. $Θ$包含有限个遍历概率;。$Θ$中的任何不变概率都是$Θ$中遍历概率的凸组合。在不变$σ$ -代数上，$Θ$中的任何概率都与$Θ$中的不变概率一致.最后一个性质已经在\textsl{Cerreia-Vioglio, Maccheroni, and Marinacci} \cite{ergodictheorem}中得到，它首次研究了这种容量的遍历性。作为该刻画的应用，我们证明了一个遍历性结果（定理\ref {improve}），它改进了\cite{ergodictheorem}中的结果，使得$ξ$的时间均值的极限由上期望$\sup_{P\inΘ}E_P[ξ]$而不是Choquet积分所约束.一般来说，前者是严格较小的。
英文摘要：
The objective of this paper is to characterize the structure of the set $Θ$ for a continuous ergodic upper probability $\mathbb{V}=\sup_{P\inΘ}P$ (Theorem \ref {main result}): . $Θ$ contains a finite number of ergodic probabilities; . Any invariant probability in $Θ$ is a convex combination of those ergodic ones in $Θ$; . Any probability in $Θ$ coincides with an invariant one in $Θ$ on the invariant $σ$-algebra. The last property has already been obtained in \textsl{Cerreia-Vioglio, Maccheroni, and Marinacci} \cite{ergodictheorem}, which firstly studied the ergodicity of such capacities. As an application of the characterization, we prove an ergodicity result (Theorem \ref {improve}), which improves the result in \cite{ergodictheorem} in the sense that the limit of the time mean of $ξ$ is bounded by the upper expectation $\sup_{P\inΘ}E_P[ξ]$, instead of the Choquet integral. Generally, the former is strictly smaller.
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。
