集值测度的Riesz表示定理

RIESZ PRESENTATION OF SET-VALUED MEASUREMENT

集值映射概念的提出始于本世纪40年代,其背景是对不动点问题的讨论。60年代以后,由于经济学发展的需要,集值映射理论得到迅速的发展,自身理论体系不断完善,发展成为一门新兴学科——集值分析学。集值分析学广泛应用于经济数学、控制论、量子统计学,并且同凸分析、概率论结合得到迅速发展。在该文中给出了集值测度的值域有界与集值测度半有界变差等价,研究了取值于自反 Banach 空间上的弱紧凸值有界集值测度的 Risez 表示定理。

The concept of set-valued reflect was risen in the forties of this century,the background was the discussion of fixed-point problems.Due to the demand of economic development the theory of set-valued reflection was developed rapidly in the sixties.With the perfecting of its theory system,it became a new mathematics branch——set-valued analysis.Set-valued analysis is widely used in economic mathematics,cybemetics and quantum statistics,its de- velopment was also.quickened by combination with convexness analysis and probability.In this thesis,we presented that the bounded value domain of set-valued measurement is equal to the bounded semi-variation of set-valued measurement,studied riesz presentation theorem of weak-compact convex-value set-valued measurement on reflexive Banach space.