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Keywords:
non-additive measure; monotone set function; condition (E); Egoroff's theorem
non-additive measure; monotone set function; condition (E); Egoroff's theorem
Summary:
In this paper, we investigate Egoroff’s theorem with respect to monotone set function, and show that a necessary and sufficient condition that Egoroff’s theorem remain valid for monotone set function is that the monotone set function fulfill condition (E). Therefore Egoroff’s theorem for non-additive measure is formulated in full generality.
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