度量空间上的Lipschitz函数  

Lipschitz Function in the Measure Space

作　　者：张露萍[1] 

机构地区：[1]江西蓝天学院复杂生命动力研究所

出　　处：《江西科技学院学报》2009年第1期26-29,共4页Journal of Jiangxi University of Technology

摘　　要：在经典的欧氏空间的条件下构造微分结构,运用Rademacher定理是一个很好的方法,如何在一般的度量空间建立微分结构,是人们关注的问题。通过研究了对度量空间的Lipschitz函数进行微分,研究这个函数类在局部的微分结构,自然的定义了一个Sobolev空间,对在度量空间上建立微分结构有一定的帮助。Using Rademacher principle is a good way of constructing differential structure in the classic Euclidean space.How to establish differential structure in a normal measure space is a problem of great concern.The paper studies the differentiation of Lipschitz in the measure space and the internal differential structure of this class of function.Also,it naturally defines Sobolev space which has some help in setting up differential structure in the measure space.

关 键 词：LIPSCHITZ 函数 度量空间 

分 类 号：O189.11[理学—数学]