由度量诱导的集合列上(下)极限及其应用  

The Super (Inferior) Limit of Sequence of Sets Inducedby a Metric and Applications

作　　者：李杰 孙明澎 LI Jie;SUN Mingpeng(School of Mathematics and Statistics,Jiangsu Normal University,Xuzhou Jiangsu 221116,China)

机构地区：[1]江苏师范大学数学与统计学院,江苏徐州221116

出　　处：《大学数学》2023年第6期46-52,共7页College Mathematics

基　　金：江苏师范大学数学与统计学院课程思政示范课程建设项目(22XYKCSZ01);国家自然科学基金重点项目(12031019);江苏师范大学科研启动基金项目(17XLR011)。

摘　　要：从数列上(下)极限出发,引入并研究由度量诱导的集合列上(下)极限,证明通常的集合列上(下)极限本质上是由离散度量诱导的上(下)极限,并且Lebesgue测度关于由度量诱导的集合列极限保持一定的连续性.Based on the super(inferior)limit of real sequence,the super(inferior)limit of sequence of sets induced by a metric is introduced and studied.It is proved that the classical super(inferior)limit of sequence of sets is essentially the super(inferior)limit of sequence of sets induced by the discrete metric,and Lebesgue measure maintains certain continuity about the limit of sequence of sets induced by a metric.

关 键 词：集合列 上(下)极限集 离散度量 勒贝格测度 连续性 

分 类 号：O174.1[理学—数学]