A Yosida–Hewitt decomposition for minitive set functions

Abstract

We prove for minitive set functions defined on a σ -algebra, a similar decomposition theorem to the Yosida–Hewitt's one for classical measures, this way any minitive set function can be decomposed in a fuzzy minitive measure part and a purely minitive part. A particular attention is given for the countable case where the canonical description of any σ -continuous necessity is fully elicited and provide a simple way to compute the Choquet integral of any bounded sequence.