Lift zonoid and barycentric representation on a Banach space with a cylinder measure
Probability
2012-11-14 v1
Abstract
We show that the lift zonoid concept for a probability measure on R^d, introduced in (Koshevoy and Mosler, 1997), leads naturally to a one-to one representation of any interior point of the convex hull of the support of a continuous measure as the barycenter w.r.t. to this measure of either of a half-space, or the whole space. We prove the infinite-dimensional generalization of this representation, which is based on the extension of the lift-zonoid concept for a cylindrical probability measure.
Keywords
Cite
@article{arxiv.1211.2927,
title = {Lift zonoid and barycentric representation on a Banach space with a cylinder measure},
author = {Alexei M. Kulik and Taras D. Tymoshkevych},
journal= {arXiv preprint arXiv:1211.2927},
year = {2012}
}