论文标题
扩展Choquet理论：痕量凸性
Extending the Choquet theory: Trace convexity
论文作者
论文摘要
我们分别为函数和紧凑型拓扑空间的子集引入了痕量凸度的概念。这个概念概括了向量空间的经典凸度，以及紧凑型度量空间的Choquet凸度。我们为集合和功能以及Krein-Milman定理提供了痕量跨性别化的新概念。我们表明，上半连续的凸 - 轨道函数的最大值在一个choquet-boundary点上达到了最大值，我们获得了最大原理的几个增强版本，这些版本将经典的鲍尔定理以及其抽象版本推广到Choquet理论中。我们用三种不同类型的具体示例来说明我们的概念和结果。
We introduce the notion of trace convexity for functions and respectively, for subsets of a compact topological space. This notion generalizes both classical convexity of vector spaces, as well as Choquet convexity for compact metric spaces. We provide new notions of trace-convexification for sets and functions as well as a general version of Krein-Milman theorem. We show that the class of upper semicontinuous convex-trace functions attaining their maximum at exactly one Choquet-boundary point is residual and we obtain several enhanced versions of the maximum principle which generalize both the classical Bauer's theorem as well as its abstract version in the Choquet theory. We illustrate our notions and results with concrete examples of three different types.
