fact: Definition hahn_decomposition d (T : semiRingOfSetsType d) (R : numFieldType) (nu : {charge set T -> \bar R}) P N := [/\ nu.-positive_set P, nu.-negative_set N, P `|` N = [set: T] & P `&` N = set0].
imports: mathcomp(all_ssreflect ssralg ssrnum ssrint interval) mathcomp(finmap fingroup perm rat) mathcomp(mathcomp_extra boolp classical_sets cardinality) mathcomp(functions fsbigop set_interval) HB(structures) reals ereal signed topology numfun normedtype sequences esum measure realfun lebesgue_measure lebesgue_integral