The paper discusses the relations between complete convergence and almost uniform convergence, almost everywhere convergence, convergence in measure of fathomable functional sequence, and presents two common properties and one decision theorem.

• 摘要讨论了可测函数序列完全收敛与几乎一致收敛、几乎处处收敛、依测度收敛之间的关系，并给出了它的两个常用性质和一个判定定理。