R^n中一般凸集上的顶点凸组合表示定理

Generalization of the Theorem that Convex Polyhedron can Be Expressed as the Convex Combinations of its Extreme Points to General Convex Set in Euclidean Space

通过对切面技术、归纳法等的创意使用,证明了R^n中凸集顶点的存在性,进而证明了R^n中一般有界闭凸集中任意一点同样可表示为顶点的凸组合.

In n-dimensional Euclidean space,using tangent plane technique,mathematical induction and so on,the existence of convex sets'extreme points is proved,and it is further proved that an arbitrary point in general bounded closed convex set(not limited to convex polyhedron)can also be expressed as a convex combination of the extreme points.