proposition: Lemma integral_ge0 D f : (forall x, D x -> 0 <= f x) -> 0 <= \int_(x in D) f x.
proof: Proof. move=> f0; rewrite ge0_integralE// nnintegral_ge0// => x. by rewrite /patch; case: ifP; rewrite // inE => /f0->. 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