Lift zonoid and barycentric representation on a Banach space with a cylinder measure

Alexei M. Kulik; Taras D. Tymoshkevych

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arXiv · 1211.2927

Lift zonoid and barycentric representation on a Banach space with a cylinder measure

Alexei M. Kulik·Taras D. Tymoshkevych

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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.

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Alexei M. Kulik, Taras D. Tymoshkevych. 2012-11-13. Lift zonoid and barycentric representation on a Banach space with a cylinder measure. https://arxiv.org/abs/1211.2927

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