Riesz表示定理的推广形式

On Extended Version of Riesz Representation Theorem

常见的Riesz表示定理的证明方法是通过在f的零空间的正交补中,构造满足表示定理公式的向量.这里给出著名的Riesz表示定理的一种推广形式,并尝试从不同的角度给出Riesz表示定理的不同证明方法.利用几何测度论的知识给出了一个直接的证明.

The proof of common Riesz representation theorem is to construct vectors satisfying the expression theorem formula through orthogonal complement vectors in zero space. We will give a generalization of the famous Riesz representation theorem and try to give different proof methods from different angles. We give a direct proof by suing the knowledge of geometric measure theory.