proposition: Lemma cvg_monotone_convergence : \int[mu]_(x in D) g' n x @[n \oo] --> \int[mu]_(x in D) f' x.
proof: Proof. rewrite monotone_convergence; apply: ereal_nondecreasing_is_cvgn => m n mn. by apply: ge0_le_integral => // t Dt; [exact: g'0|exact: g'0|exact: nd_g']. 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