proposition: Lemma integrable_sum (s : seq (T -> \bar R)) : (forall h, h \in s -> mu_int h) -> mu_int (fun x => \sum_(h <- s) h x).
proof: Proof. elim: s => [_|h s ih hs]. by under eq_fun do rewrite big_nil; exact: integrable0. under eq_fun do rewrite big_cons; apply: integrableD => //. - by apply: hs; rewrite in_cons eqxx. - by apply: ih => k ks; apply: hs; rewrite in_cons ks orbT. 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