A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is
Suppose d + 1 absolutely continuous probability measures m 0 ,. .. , m d on R d are given. In this paper, we prove that there exists a point of R d that belongs to the convex hull of d + 1 points v 0 ,. .. , v d with probability at least 2d (d+1)!(d+1) , where each point v i is sampled independently according to probability measure m i .fatcat:2xj2tm4zgngonnzocahferw2ha