proposition: Lemma integral_setI_indic (E D : set T) (mD : measurable D) (f : T -> \bar R) : measurable E -> \int[mu]_(x in E `&` D) f x = \int[mu]_(x in E) (f x * (\1_D x)%:E).
proof: Proof. move=> mE; rewrite integral_mkcondr; apply: eq_integral => x xE. by rewrite indic_restrict /patch; case: ifPn; rewrite ?mule1 ?mule0. 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