proposition: Lemma measurable_fun_fRN : measurable_fun [set: T] fRN.
proof: Proof. rewrite (_ : fRN = fun x => limn_esup (F ^~ x)). apply: measurable_fun_limn_esup => // n. exact: measurable_max_approxRN_seq. apply/funext=> n; rewrite is_cvg_limn_esupE//. exact: is_cvg_max_approxRN_seq. 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