@inproceedings{2418,
abstract = {For an absolutely continuous probability measure μ on Rd and a nonnegative integer k, let sk(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 sk(μ, 0), and we characterize the measures in Rd which attain this bound. 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 for simplicial convex polytopes.},
author = {Uli Wagner and Welzl, Emo},
pages = {50 -- 56},
publisher = {ACM},
title = {{Origin-embracing distributions or a continuous analogue of the Upper Bound Theorem}},
doi = {10.1145/336154.336176},
year = {2000},
}