Egorov theorem; fuzzy set; measure theory; monotone function
Independently with  a corresponding fuzzy approach has been developed in [3-5] with applications in measure theory. One of the results the Egoroff theorem has been proved in an abstract form. In  a necessary and sufficient condition for holding the Egoroff theorem was presented in the case of a space with a monotone measure. By the help of  and  we prove a variant of the Egoroff theorem stated in .