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A further investigation for Egoroff’s theorem with respect to monotone set functions. (English) Zbl 1249.93044
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.

93B25 Algebraic methods
15A06 Linear equations (linear algebraic aspects)
06F05 Ordered semigroups and monoids
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