一句话：将标记马尔可夫过程中行为等价可构造互模拟 semipullback 的结果推广到更广的可测空间。
标记马尔可夫过程（LMP）由可测空间及一族 Markov kernel 组成，用于建模概率计算。其核心问题是判断两个 LMP 是否行为相同：互模拟要求存在共同的 LMP 通过保测映射分别映射到二者，行为等价则要求存在共同的余锥。二者对一般可测空间不等价；Doberkat 在 Edalat 工作基础上证明，对 analytic Borel 空间二者一致，且可从行为等价图构造出交换的 semipullback。本文把该结果推广到与 Polish 空间的普遍可测子集同构、并带上 Borel σ-代数迹的可测空间。证明使用 Strassen 定理的一个版本，处理有限可加测度的共同扩展，从而在更广空间类上得到所需的 semipullback。
A labelled Markov process (LMP) consists of a measurable space $S$ together with an indexed family of Markov kernels from $S$ to itself. This structure has been used to model probabilistic computations in Computer Science, and one of the main problems in the area is to define and decide whether two LMP $S$ and $S'$ "behave the same". There are two natural categorical definitions of sameness of behavior: $S$ and $S'$ are bisimilar if there exist an LMP $ T$ and measure preserving maps forming a diagram of the shape $ S\leftarrow T \rightarrow{S'}$; and they are behaviorally equivalent if there exist some $ U$ and maps forming a dual diagram $ S\rightarrow U \leftarrow{S'}$. These two notions differ for general measurable spaces but Doberkat (extending a result by Edalat) proved that they coincide for analytic Borel spaces, showing that from every diagram $S\rightarrow U \leftarrow{S'}$ one can obtain a bisimilarity diagram as above. Moreover, the resulting square of measure preserving maps is commutative (a semipullback). In this paper, we extend the previous result to measurable spaces $S$ isomorphic to a universally measurable subset of a Polish space with the trace of the Borel $\sigma$-algebra, using a version of Strassen's theorem on common extensions of finitely additive measures.