Continuous valuations on the space of Lipschitz functions on the sphere

Autor:	Colesanti, Andrea, Pagnini, Daniele, Tradacete, Pedro, Villanueva, Ignacio
Rok vydání:	2020
Předmět:	Mathematics - Metric Geometry Mathematics - Functional Analysis 52B45 26A16 28A12
Druh dokumentu:	Working Paper
Popis:	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. Comment: 35 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2005.05419 Zobrazit plný text záznamu View this record from Arxiv