proposition: Lemma integral_fune_fin_num (f : T -> \bar R) : mu.-integrable D f -> \int[mu]_(x in D) f x \is a fin_num.
proof: Proof. move=> h; apply/fin_numPlt; rewrite integral_fune_lt_pinfty// andbC/= -/(- +oo). rewrite lteNl -integralN; first exact/integral_fune_lt_pinfty/integrableN. by rewrite fin_num_adde_defl// fin_numN integrable_neg_fin_num. 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