proposition: Lemma additive_nnsfunr (g f : {nnsfun T >-> R}) x : \sum_(i \in range g) m (f @^-1` [set x] `&` (g @^-1` [set i])) = m (f @^-1` [set x] `&` \big[setU/set0]_(i \in range g) (g @^-1` [set i])).
proof: Proof. rewrite -?measure_fsbig//. - by rewrite !fsbig_finite//= big_distrr//. - by move=> i Ai; apply: measurableI => //. - exact/trivIset_setIl/trivIset_preimage1. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrnum ssrint interval finmap) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality fsbigop ) signed reals ereal topology normedtype sequences real_interval esum measure lebesgue_measure numfun