随机度量理论及其应用

Random Metric Theory and Its Applications

扼要地总结作者近 10多年来在从事随机度量理论及其应用过程中所获得的主要结果与思想 ,包括 1)关于随机度量理论与随机泛函分析的整体关系 ,并给出对应于随机度量理论标准定义的随机共轭空间理论 (此部分工作系作者最近的成果 ) ;2 )随机度量理论的一个新的版本及对应于这个版本下随机共轭空间理论的基本结果 ;3)关于随机共轭空间的表示定理 ;4 )关于完备随机赋范模为随机自反空间的特征化定理 ;5)结束语 .

The central purpose of this paper is to give a brief survey of the principal results and ideas the author obtained in the course of undertaking the study of random metric theory and its applications. This paper is divided into five parts:Part 1 is devoted to the global relationship between random metric theory and random functional analysis,and a new type of the theory of random conjugate spaces corresponding to the original version of random metric theory; Part 2 to a new version of random metric theory together with the theory of random conjugate spaces corresponding to the new version; Part 3 to representation theorems for random conjugate spaces; Part 4 to characterizations for a complete random normed module to be random reflexive; Part 5 to concluding remarks.