概率测度集上的模糊Prokhorov度量

On balanced capacities

We consider capacity (fuzzy measure, non-additive probability) on a compactum as a monotone cooperative normed game. Then it is naturally to consider probability measures as elements of core of such game. We prove an analogue of Bondareva-Shapley theorem that non-emptiness of the core is equivalent to balancedness of the capacity. We investigate categorical properties of balanced capacities and give characterizations of some fuzzy integrals of balanced capacities.

关于精确容量

On exact capacities

本文将容量视为单调合作规范游戏，引入拓扑学中的精确游戏类，并证明其为容量 functor 的子functor，介于凸容量和平衡容量之间，同时探讨概率测度作为游戏核心元素的表示及精确容量的开放性。