If ${\mathfrak {F}}$ is a type-definable family of commensurable subsets, subgroups or subvector spaces in a metric structure, then there is an invariant subset, subgroup or subvector space commensurable with ${\mathfrak {F}}$. This in particular applies to type-definable or hyper-definable objects in a classical first-order structure.

中文翻译：

---

施利希廷定理的度量版本

如果${\mathfrak {F}}$是度量结构中可通约子集、子群或子向量空间的类型可定义族，则存在可与${\mathfrak {F}}$. 这尤其适用于经典一阶结构中的类型可定义或超可定义对象。