球面上Lipschitz函数空间的连续赋值
Continuous valuations on the space of Lipschitz functions on the sphere
摘要：
研究了欧氏单位球面$S^{n-1}$上Lipschitz函数空间上的实值赋值.在引入一个适当的收敛概念后，我们证明了连续赋值是有界的，它是有界的Lipschitz范数。这一事实，结合措施的理论论据，将产生一个整表示的连续和旋转不变的估值空间的Lipschitz函数在1维领域。
英文摘要：
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.
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