In a metric space $(\mathrm{\Omega },d)$, coherent upper conditional previsions are defined by Hausdorff outer measures on the linear space of all absolutely Choquet integrable random variables. They are proven to satisfy the disintegration property on every non-null partition if Ω is a set with positive and finite Hausdorff outer measure in its Hausdorff dimension. Coherent upper conditional probabilities are obtained as restrictions to the indicators function and it is proven they can be extended as finitely additive probabilities in the sense of Dubins. Examples are given in the discrete metric space and in the Euclidean metric space.

中文翻译：

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关于无界随机变量的Hausdorff外部测度的相干上限条件预设的崩解性质

在公制空间 $（\mathrm{\Omega }，d）$在所有绝对Choquet可积随机变量的线性空间上，由Hausdorff外部测度定义相干的条件上限。如果Ω是在Hausdorff维度上具有正且有限的Hausdorff外部度量的集合，则证明它们可以满足每个非空分区的崩解特性。获得了相关的上限条件概率作为对指标功能的限制，并且证明了可以将它们扩展为杜宾斯意义上的有限加性概率。在离散度量空间和欧几里德度量空间中给出了示例。