In this note, we show a generalized version of convergence in measure theorem of Sugeno integrals in the framework concerning ordered pair of monotone measures. The condition of a kind of absolute continuity we employed is not only sufficient, but also necessary for the generalized version. The previous two versions (standard-form and pseudo-form) of the convergence in measure theorem are recovered by this generalized version. Thus, the convergence in measure theorems of Sugeno integrals are unified in general framework. In the same way the convergence in measure theorem and strict convergence in measure theorem of seminnormed fuzzy integrals are generalized, respectively. The relations between the convergence in measure and the convergence pseudo-in measure of measurable functions sequence are described in the context relating to a pair of monotone measures.

在本说明中，我们展示了关于有序单调测度对的框架中 Sugeno 积分测度定理收敛的广义版本。我们采用的一种绝对连续性的条件对于广义版本不仅是充分的，而且是必要的。这个广义版本恢复了测度定理收敛的前两个版本（标准形式和伪形式）。这样，Sugeno 积分测度定理的收敛性在一般框架中是统一的。同理，测度定理的收敛性和测度定理的严格收敛性的半规范模糊积分分别被推广。在与一对单调测度相关的上下文中描述了测度收敛与可测函数序列的收敛伪入测度之间的关系。