论文标题
在Lipschitz的空间上的连续估值在球体上的功能
Continuous valuations on the space of Lipschitz functions on the sphere
论文作者
论文摘要
我们研究了关于Lipschitz功能在Euclidean单位球体$ s^{n-1} $上的实现估值。在引入了适当的收敛概念之后，我们表明连续估值在相对于Lipschitz Norm有限的集合上有限。这一事实将结合度量理论参数结合在一起，将产生在Lipschitz函数上一维球体的函数空间上的连续和旋转不变估值的整体表示。
We study real-valued valuations on the space of Lipschitz functions over the Euclidean unit sphere $S^{n-1}$. After introducing an appropriate notion of convergence, we show that continuous valuations are bounded on sets which are bounded with respect to the Lipschitz norm. This fact, in combination with measure theoretical arguments, will yield an integral representation for continuous and rotation invariant valuations on the space of Lipschitz functions over the 1-dimensional sphere.
