摘要
有限测度集上,可测函数列依测度收敛乘除在一定条件下恒成立.给出反例论证定义在无限测度集合上两可测函数列依测度收敛乘除在与有限测度相关结论相同条件下不成立.通过进一步探讨,得到了在集合测度为无限时相应结论成立的一个较宽松条件,并且对这一条件给出了易于验证的等价形式.
On finite measurable set, convergence in measure of the measurable function sequence can be multiplicated and divided under appropriate condition. The article enumerates the reverse examples to illustrate the relevant conclusions are not correct on infinite measurable set under the same conditions. According to further discussion, it obtains a looser condition which ensures the relevant conclusions correct on infinite measurable set. Also, it gives the equivalent form verified easily for the condition.
出处
《华中师范大学学报（自然科学版）》
CAS
CSCD
2007年第1期28-30,共3页
Journal of Central China Normal University：Natural Sciences
基金
国家自然科学基金重点项目资助(10431060)
关键词
可测函数列
依测度收敛
几乎处处收敛
测度空间
几乎处处有限
measurable function sequence
convergence in measure
convergence almost everywhere
measure space
finite almost everywhere
