【摘要】 本文讨论了完全收敛性与可测函数序列依测度收敛、几乎处处收敛以及强收敛之间的等价关系,并且给出了依测度收敛、几乎处处收敛与完全收敛之间等价的充分必要条件,即fn(x)单调增加,并且(An)两两不相交,其中An=[|fn-f|≥ε],ε>0。更多还原

【Abstract】 The paper discusses the equivalent relationship between complete convergence and convergence in measure,almost everywhere convergence,strong convergence of fathomable functional sequence,and presentes a necessary and sufficient condition when convergence in measure and almost everywhere convergence are equivalent to complete convergence,namely,fn(s) monotone increasing,and(An) pairwise disjoint,where An=[|fn-f|≥ε],ε>0.更多还原