摘要
函数列{xn}的收敛性,说明:函数列的收敛域一般是定义域的子集;函数列虽然不一致收敛,但其极限函数可以是连续的;极限运算也可以与积分运算交换运算及求导运算交换运算的次序,并由此引出了函数列一致收敛与几乎处处收敛的概念,论述了叶果洛夫(Егоров)定理的建立与证明思路,充分说明了函数列{xn}在分析数学中的作用,诠释了数学概念、抽象与简单的辩证关系.
Based on detailed analysis, this paper concludes that generally the convergence domain of the sequence of functions is the subset of the domain of the definition. Though the sequence of functions is not a uniform convergence, its limit function is continuous. The order of operation can be exchanged with integral operation and derivation operation, then the concepts of almost everywhere convergence and eve- rywhere convergence are introduced. Then, it discusses the construction and thoughts of proving the EropoB＇ s Theorem, and gives a full analysis of sequence of function { xn } in analytical mathematics. Finally, it explains some abstract concepts and theorems by using simple examples.
出处
《陇东学院学报》
2008年第5期1-3,共3页
Journal of Longdong University
基金
陇东学院青年科技创新项目(XYZK0714)
关键词
函数列
收敛域
几乎处处收敛
处处收敛
一致收敛
测度
叶果洛夫(EropoB)定理
sequence of functions
convergence domain
almost everywhere converge
everywhere converge
uniform convergence
measure
Eropon＇ s theorem
