关于随机光滑点

Random Smooth Points

提出随机赋范模中随机光滑点的概念,利用随机赋范模与经典赋范空间的联系,给出了随机光滑点和经典光滑点的关系。最后,利用有限生成随机赋范模的代数结构,给出了几个随机光滑点的基本性质。这些结果将进一步丰富随机赋范模几何学已有的内容。

The definition of random smooth points was presented in random normed modules. By using the relations between random normed modules and classical normed spaces,the intrinsic relations between random smooth points in random normed modules and smooth points in normed spaces were obtained. Finally,by using the algebraic structure of finitely generated random normed modules,some basic properties of random smooth points were gotten. These results further enrich existing content of geometry in random normed modules.