engleski

The general integral form of Jensen's inequality

The aim of this presentation is to show the integral form of Jensen’s inequality for convex functions of several variables as general as possible. In this regard, we have to rely on the decomposition of a nonempty convex set C in the n-dimensional space R^n using concepts of the relative interior of C, and k-faces of C including extreme points as 0-faces. A nonempty convex set C in R^n can be represented as the union of pairwise disjoint relative interiors of its k-faces for those integers k between 0 and n for which k-faces exist. Such a union can be finite (tetrahedron in R^3) or infinite (cone in R^3).

convex set, convex function of several variables, Jensen's inequality

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