We study real-valued valuations on the space of Lipschitz functions over the Euclidean unit sphere. 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.

Continuous valuations on the space of Lipschitz functions on the sphere / Andrea Colesanti, Daniele Pagnini, Pedro Tradacete, Ignacio Villanueva. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - ELETTRONICO. - 280:(2021), pp. 1-43. [10.1016/j.jfa.2020.108873]

Continuous valuations on the space of Lipschitz functions on the sphere

Andrea Colesanti;
2021

Abstract

We study real-valued valuations on the space of Lipschitz functions over the Euclidean unit sphere. 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.
2021
280
1
43
Andrea Colesanti, Daniele Pagnini, Pedro Tradacete, Ignacio Villanueva
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1222823
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