proposition: Lemma int_fRN_ub A : measurable A -> \int[mu]_(x in A) fRN x <= nu A.
proof: Proof. move=> mA; rewrite int_fRN_lim// lime_le //. exact: is_cvg_int_max_approxRN_seq. by apply: nearW => n; exact: int_F_nu. Qed.
imports: mathcomp(all_ssreflect ssralg ssrnum ssrint interval) mathcomp(finmap fingroup perm rat) mathcomp(mathcomp_extra boolp classical_sets cardinality) mathcomp(functions fsbigop set_interval) HB(structures) reals ereal signed topology numfun normedtype sequences esum measure realfun lebesgue_measure lebesgue_integral