We establish a dilation-theoretic characterization of the Choquet order on the space of measures on a compact convex set using ideas from the theory of operator algebras. This yields an extension of Cartier's dilation theorem to the non-separable case, as well as a non-separable version of Šaškin's theorem from approximation theory. We show that a slight variant of this order characterizes the representations of a commutative C*-algebras that have the unique extension property relative to a set of generators. This reduces the commutative case of Arveson's hyperrigidity conjecture to the question of whether measures that are maximal with respect to the classical Choquet order are also maximal with respect to this new order. An example shows that these orders are not the same in general.

我们根据算子代数理论的思想，在紧凸集上的测度空间上建立了Choquet阶的扩张理论。这将卡地亚的扩张定理扩展到不可分的情况，以及从近似理论出发的舍什金定理的不可分形式。我们表明，此顺序的微小变化代表了可交换C *代数的表示形式，这些C *代数相对于一组生成器具有唯一的扩展性质。这将Arveson的超刚性猜想的可交换情况简化为以下问题：相对于经典Choquet阶最大的度量是否相对于这个新阶也最大。一个例子表明，这些顺序通常是不同的。