可测空间上复值可测函数列的统计收敛与经典收敛关系

The Relation of Statistical Convergence and Classical Convergence of Complex-valued Measurable Functions on Measurable Space

证明了可测空间(x,μ)上统计收敛的复值可测函数列一定存在某一子列几乎处处收敛;反之,若复值可测函数列几乎处处收敛必定能推出其是统计收敛的,也必定是依测度收敛的.

The fact that there is one subsequence which is almost convergence of complex-valued measurable functions which are statistical convergence on measurable space（X,μ） was proved.There is one subsequence which is almost convergence of complex-valued measurable functions which is measure convergence.Contrarily,complex-valued measurable functions which were almost convergence must be statistical convergence and measure convergence.