Set-valued Lusin type theorem for null–null-additive set multifunctions

Abstract

In a previous paper, we presented a set-valued Egoroff type theorem for monotone set multifunctions. In this paper, a new version of this set-valued Egoroff type theorem is obtained. It enables a set-valued Lusin type theorem for null–null-additive monotone continuous set multifunctions to be established. Several applications of this Lusin type theorem are given. Pointing out some relationships among μ-measurability, A-measurability and totally measurability of real functions, we also compare our new Lusin type theorem with Lusin's theorem previously obtained by the second author.