@article{2419,
  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.},
  author       = {Wagner, Uli and Welzl, Emo},
  issn         = {0179-5376},
  journal      = {Discrete & Computational Geometry},
  number       = {2},
  pages        = {205 -- 219},
  publisher    = {Springer},
  title        = {{A continuous analogue of the Upper Bound Theorem}},
  doi          = {10.1007/s00454-001-0028-9},
  volume       = {26},
  year         = {2001},
}