proposition: Lemma integral_indic (E : set T) : measurable E -> \int[mu]_(x in D) (\1_E x)%:E = mu (E `&` D).
proof: Proof. move=> mE; rewrite (_ : \1_E = indic_nnsfun R mE)// integral_nnsfun//=. by rewrite restrict_indic sintegral_indic//; exact: measurableI. 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