一句话：为马尔可夫过程建立无受限 Stone 型对偶，扩展 Sikorski 可测空间对偶并清晰刻画事件互模拟。
Stone 对偶联系布尔代数与空间，在计算机科学中广泛用于理解计算模型与其推理语言之间的关系。近期概率过程研究已为受限马尔可夫过程建立 Stone 型对偶，其对偶范畴是 Aumann 代数，即带有一族以有理概率为索引的可数模态的布尔代数。本文考虑 Aumann 代数的一种替代定义，由此得到马尔可夫过程的 dual adjunction，并对实践中许多可测空间构成对偶，从而扩展了 Sikorski 的可测空间对偶。该定义不要求概率模态保持某个区分的 clopen 基，也不要求马尔可夫过程态射保持该基。额外的一般性使作者能够给出 Aumann 代数上事件互模拟的一个清晰定义。
Stone duality relates logic, in the form of Boolean algebra, to spaces. Stone-type dualities abound in computer science and have been of great use in understanding the relationship between computational models and the languages used to reason about them. Recent work on probabilistic processes has established a Stone-type duality for a restricted class of Markov processes. The dual category was a new notion—Aumann algebras—which are Boolean algebras equipped with countable family of modalities indexed by rational probabilities. In this article we consider an alternative definition of Aumann algebra that leads to dual adjunction for Markov processes that is a duality for many measurable spaces occurring in practice. This extends a duality for measurable spaces due to Sikorski. In particular, we do not require that the probabilistic modalities preserve a distinguished base of clopen sets, nor that morphisms of Markov processes do so. The extra generality allows us to give a perspicuous definition of event bisimulation on Aumann algebras.