Variational Analysis
Carathéodory's Theorem states that if a point belongs to the convex hull of a set of points in a Euclidean space, then it can be expressed as a convex combination of at most $d+1$ points from that set, where $d$ is the dimension of the space. This theorem highlights the fundamental relationship between convex sets and the representation of points within those sets, serving as a cornerstone in understanding the structure of convex functions and multifunctions.
congrats on reading the definition of Carathéodory's Theorem. now let's actually learn it.