Lithuanian Mathematical Journal

, Volume 53, Issue 2, pp 181–195 | Cite as

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



We show that the lift zonoid concept for a probability measure on \( {{\mathbb{R}}^d} \), introduced in [G.A. Koshevoy and K. Mosler, Zonoid trimming for multivariate distributions, Ann. Stat., 25(5):1998–2017, 1997], naturally leads to a oneto-one representation of any interior point of the convex hull of the support of a continuous measure as the barycenter w.r.t. 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.


zonoid lift zonoid cylinder measure barycentric representation 


primary 60D05 secondary 28C20 


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institute of MathematicsNational Academy of Sciences of UkraineKyivUkraine
  2. 2.Taras Shevchenko National University of KyivKyivUkraine

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