中文摘要：

定义了伪条件（M）和伪Egoroff条件,证明了在非可加测度理论上伪Egoroff条件与Egoroff定理的一种伪形式等价,伪条件（M）是伪Egoroff条件的一个必要条件,以及Egoroff定理的上述伪形式是伪条件（M）的一个必要条件,从而得到了在非可加测度空间上Egoroff定理四种形式的等价条件。

英文摘要：

The pseudo-condition（M）and the pseudo-Egoroff condition are given in this note.The necessary and sufficient conditions for the four kinds of Egoroff＇s theorems on non-additive measure space are got by proving the pseudo-Egoroff condition is equivalent to a pseudo form of Egoroff＇s theorem,and a necessary condition of the pseudo-condition（M）is the pseudo-Egoroff condition,and a necessary condition of the the above pseudo form of Egoroff＇s theorem is the pseudo-conditionm（M）.