proposition: Lemma ysection_ndseq_closed : ndseq_closed B.
proof: Proof. move=> F ndF; rewrite /B /= => BF; split. by apply: bigcupT_measurable => n; have [] := BF n. have psiF x : psi (F i) x @[i \oo] --> psi (\bigcup_i F i) x. rewrite /psi /= ysection_bigcup; apply: nondecreasing_cvg_mu. - by move=> n; apply: measurable_ysection; case: (BF n). - by apply: bigcupT_measurable => i; apply: measurable_ysection; case: (BF i). - by move=> m n mn; exact/subsetPset/le_ysection/subsetPset/ndF. apply: (emeasurable_fun_cvg (psi \o F)) => //. - by move=> i; have [] := BF i. - by move=> x _; exact: psiF. 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