proposition: Lemma integral_set0 (f : T -> \bar R) : \int[mu]_(x in set0) f x = 0.
proof: Proof. rewrite integral_mkcond integral0_eq// => x _. by rewrite /restrict; case: ifPn => //; rewrite in_set0. 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