论文标题
riesz空间中的KAC公式和庞加莱复发定理
The Kac formula and Poincaré recurrence theorem in Riesz spaces
论文作者
论文摘要
Riesz空间（非点）概括是针对复发概念，首次复发和有条件的真实性提供的。开发了Poincaré复发定理和KAC公式的Riesz空间条件版本。在温和的假设下，证明每个条件期望保存过程在与该过程的迭代相关的cesàRO产生的条件期望方面都是有条件的。应用于$ l^1（ω，{\ Mathcal a}，μ）$中的过程，其中$μ$是一种概率度量，获得了上述定理的新条件版本。
Riesz space (non-pointwise) generalizations for iterative processes are given for the concepts of recurrence, first recurrence and conditional ergodicity. Riesz space conditional versions of the Poincaré Recurrence Theorem and the Kac formula are developed. Under mild assumptions, it is shown that every conditional expectation preserving process is conditionally ergodic with respect to the conditional expectation generated by the Cesàro mean associated with the iterates of the process. Applied to processes in $L^1(Ω,{\mathcal A},μ)$, where $μ$ is a probability measure, new conditional versions of the above theorems are obtained.
