proposition: Lemma xsection_ndseq_closed : ndseq_closed B.
proof: Proof. move=> F ndF; rewrite /B /= => BF; split. by apply: bigcupT_measurable => n; have [] := BF n. have phiF x : phi (F i) x @[i \oo] --> phi (\bigcup_i F i) x. rewrite /phi /= xsection_bigcup; apply: nondecreasing_cvg_mu. - by move=> n; apply: measurable_xsection; case: (BF n). - by apply: bigcupT_measurable => i; apply: measurable_xsection; case: (BF i). - by move=> m n mn; exact/subsetPset/le_xsection/subsetPset/ndF. apply: (emeasurable_fun_cvg (phi \o F)) => //. - by move=> i; have [] := BF i. - by move=> x _; exact: phiF. 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