diff --git a/Lebesgue/measurable_Rbar.v b/Lebesgue/measurable_Rbar.v index f9f788b43bcb097c10de5340577c4e695c08d747..5f18903819109133bb893e57da4e552f418e1a45 100644 --- a/Lebesgue/measurable_Rbar.v +++ b/Lebesgue/measurable_Rbar.v @@ -158,7 +158,6 @@ Qed. Lemma measurable_Rbar_Borel_correct : measurable_Rbar_Borel = measurable_Borel_Rbar. Proof. -(* apply Ext_equiv; split. (* *) rewrite measurable_Rbar_Borel_eq; unfold measurable_Borel_Rbar, measurable_Borel. @@ -166,7 +165,7 @@ intros B HB. induction HB as [A HA | A HA | A HA | A HA]; rewrite measurable_R_eq_Borel in HA. (* . *) induction HA as [A HA | | A HA1 HA2 | A HA1 HA2]. -rewrite <- Rbar_subset_open_correct; apply measurable_gen; apply RbSO_bounded; easy. +rewrite <- Rbar_subset_open_correct; apply measurable_gen; apply RbSO_woinf; easy. admit. (* rewrite up_id_empty. does not work! R vs R_UniformSpace... *) rewrite up_id_compl; apply measurable_compl. admit. @@ -184,22 +183,20 @@ rewrite <- Rbar_subset_open_correct. intros A HA; induction HA as [A HA | B HB]. (* . *) apply measurable_Rbar_Borel_R_open; easy. -induction HB as [A a HA | | ]. (* . *) +induction HB as [A B HA HB | A a b HA]. +(* .. *) apply measurable_Rbar_Borel_union. apply measurable_Rbar_Borel_R_open; easy. -apply measurable_Rbar_Borel_lt. -(* . *) -apply measurable_Rbar_Borel_union. +induction HB as [b Hb | a Ha]. apply measurable_Rbar_Borel_gt. -apply measurable_Rbar_Borel_R_open; easy. -(* . *) +apply measurable_Rbar_Borel_lt. +(* .. *) apply measurable_Rbar_Borel_union. apply measurable_Rbar_Borel_union. -apply measurable_Rbar_Borel_gt. apply measurable_Rbar_Borel_R_open; easy. +apply measurable_Rbar_Borel_gt. apply measurable_Rbar_Borel_lt. -*) Admitted. End measurable_Rbar_Borel_Facts.