论文标题
随机集和choquet型表示
Random sets and Choquet-type representations
论文作者
论文摘要
作为对凸组合的适当概括，我们介绍了所谓的Choquet组合，Choquet分解和Choquet凸出分解，以及它们在Lebesgue-Bochner空间的功率集上的相应船体操作员。我们表明，Choquet Hull与凸壳在有限维度的环境中相吻合，但是Choquet Hull在无限维度上往往更大。我们还提供了Choquet Hull的定量表征。此外，我们表明，套装的Choquet可分解船体与其（强烈的）封闭的可分解船体和Choquet凸凸的可分解船体相吻合，与凸壳的Choquet可分解船体相吻合。事实证明，所有可测量选择的闭合值多功能的集合都是可分解的，而封闭凸v值的多功能的收集是Choquet coquet convex demopsoposobable。最后，我们研究了Choquet分解和Choquet凸凸的可分解船体运算符的操作型特征。
As appropriate generalizations of convex combinations with uncountably many terms, we introduce the so-called Choquet combinations, Choquet decompositions and Choquet convex decompositions, as well as their corresponding hull operators acting on the power sets of Lebesgue-Bochner spaces. We show that Choquet hull coincides with convex hull in the finite-dimensional setting, yet Choquet hull tends to be larger in infinite dimensions. We also provide a quantitative characterization of Choquet hull. Furthermore, we show that Choquet decomposable hull of a set coincides with its (strongly) closed decomposable hull and the Choquet convex decomposable hull of a set coincides with its Choquet decomposable hull of the convex hull. It turns out that the collection of all measurable selections of a closed-valued multifunction is Choquet decomposable and those of a closed convex-valued multifunction is Choquet convex decomposable. Finally, we investigate the operator-type features of Choquet decomposable and Choquet convex decomposable hull operators when applied in succession.
