proposition: Lemma integrable_pos_fin_num f : mu_int f -> \int[mu]_(x in D) f^\+ x \is a fin_num.
proof: Proof. move=> /integrableP fi. rewrite fin_numElt; apply/andP; split. by rewrite (@lt_le_trans _ _ 0) ?lte_ninfty//; exact: integral_ge0. case: fi => mf; apply: le_lt_trans; apply: ge0_le_integral => //. - exact/measurable_funepos. - exact/measurableT_comp. - by move=> x Dx; rewrite -/((abse \o f) x) (fune_abse f) leeDl. 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