The condition of multiplicating and dividing the convergence in measure of the measurable function sequence on infinite measurable set
Wang Wen-jun · 2007
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.