与依测度收敛有关的若干反例  

Some Counterexamples Related to Convergence in Measure

作　　者：李翠香[1] 齐秋兰[1] LI Cuixiang;QI Qiulan(School of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,China)

机构地区：[1]河北师范大学数学科学学院,河北石家庄050024

出　　处：《高等数学研究》2023年第1期62-63,F0003,共3页Studies in College Mathematics

基　　金：河北省教育厅重点基金项目(ZD2019053);河北师范大学教学改革研究项目(2020XJJG059)。

摘　　要：本文通过构造反例来进一步探究依测度收敛与处处收敛的关系,依测度收敛对乘法、除法、复合运算的封闭性,以及对可测集的可数可加性等性质.In this paper, some counterexamples are constructed to further explore the properties of convergence in measure, including the relationship between convergence in measure and convergence everywhere, the closeness of convergence in measure with regard to multiplication, division and composition operations, and the countable additivity of measurable sets.

关 键 词：依测度收敛 处处收敛 封闭性 反例 

分 类 号：O174.12[理学—数学]