proposition: Lemma measure_semi_additive_ord_I (F : nat -> set T) (n : nat) : (forall k, (k < n)%N -> measurable (F k)) -> trivIset `I_n F -> measurable (\big[setU/set0]_(k < n) F k) -> mu (\big[setU/set0]_(i < n) F i) = \sum_(i < n) mu (F i).
proof: Proof. move=> mF tF; apply: measure_semi_additive_ord. by move=> k; apply: mF. by rewrite trivIset_comp// ?(image_eq [surjfun of val])//; apply: 'inj_val. Qed.
imports: mathcomp(all_ssreflect all_algebra finmap) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality fsbigop ) reals ereal signed topology normedtype sequences esum numfun HB(structures)