摘要
Егоров定理是实变函数理论中一个极其重要的定理,对于它的建立与证明方法的探讨是有必要的.在分析数学中一致收敛的重要性及几乎处处收敛不一定能够一致收敛.为了弄清楚在什么条件下几乎处处收敛能够转化为一致收敛,细致地解剖了一个典型反例,由此得到启发建立了Егоров定理,并论述了定理证明的思路与方法.最后从几个方面进行了详细的注解,交代了下一步的任务.
Егоров theorem is a significant theorem in the theory of functions of Real variable and it is very necessary to probe its establishment and method. To make sure under what circumstances everywhere converge can be converted into uniform convergence, a typical counter-case has to be analysed. Thus EropoB theorem has been set up and approaches to prove the theorem has been discussed.
出处
《陇东学院学报》
2008年第2期102-104,共3页
Journal of Longdong University
关键词
一致收敛
处处收敛
几乎处处收敛
测度
可测函数
uniform convergence
everywhere converge
almost everywhere converge
measure
measurable function
