---
res:
  bibo_abstract:
  - For an absolutely continuous probability measure μ. on ℝd and a nonnegative integer
    k, let S̃k(μ, 0) denote the probability that the convex hull of k + d + 1 random
    points which are i.i.d. according to μ contains the origin 0. For d and k given,
    we determine a tight upper bound on S̃k(μ, 0), and we characterize the measures
    in ℝd which attain this bound. As we will see, this result can be considered a
    continuous analogue of the Upper Bound Theorem for the maximal number of faces
    of convex polytopes with a given number of vertices. For our proof we introduce
    so-called h-functions, continuous counterparts of h-vectors of simplicial convex
    polytopes.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Uli
      foaf_name: Wagner, Uli
      foaf_surname: Wagner
      foaf_workInfoHomepage: http://www.librecat.org/personId=36690CA2-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-1494-0568
  - foaf_Person:
      foaf_givenName: Emo
      foaf_name: Welzl, Emo
      foaf_surname: Welzl
  bibo_doi: 10.1007/s00454-001-0028-9
  bibo_issue: '2'
  bibo_volume: 26
  dct_date: 2001^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0179-5376
  dct_language: eng
  dct_publisher: Springer@
  dct_title: A continuous analogue of the Upper Bound Theorem@
...