Editing Convex hull (section)

===Extreme points===
{{main|Krein–Milman theorem}}
An [[extreme point]] of a convex set is a point in the set that does not lie on any open line segment between any other two points of the same set.
For a convex hull, every extreme point must be part of the given set, because otherwise it cannot be formed as a convex combination of given points.
According to the [[Krein–Milman theorem]], every compact convex set in a Euclidean space (or more generally in a [[locally convex topological vector space]]) is the convex hull of its extreme points.<ref>{{harvtxt|Krein|Milman|1940}}; {{harvtxt|Lay|1982}}, p. 43.</ref> However, this may not be true for convex sets that are not compact; for instance, the whole Euclidean plane and the open unit ball are both convex, but neither one has any extreme points. [[Choquet theory]] extends this theory from finite convex combinations of extreme points to infinite combinations (integrals) in more general spaces.{{sfnp|Okon|2000}}