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Lift zonoid and barycentric representation on a Banach space with a cylinder measure. (English) Zbl 1273.60017

Summary: We show that the lift zonoid concept for a probability measure on \(\mathbb R^d\), introduced in [G. Koshevoy and K. Mosler [Bernoulli 4, No. 3, 377–399 (1998; Zbl 0945.52006)], naturally leads to a one-to-one representation of any interior point of the convex hull of the support of a continuous measure as the barycenter with respect to this measure of either a half-space or the whole space. We prove an infinite-dimensional generalization of this representation, which is based on the extension of the concept of lift zonoid for a cylindrical probability measure.

MSC:

60D05 Geometric probability and stochastic geometry
28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)

Citations:

Zbl 0945.52006
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References:

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