Merge pull request #595 from math-comp/measure_20220311

fixes #566

Author: CohenCyril

CHANGELOG_UNRELEASED.md

@@ -48,6 +48,12 @@
   + `oinv_valLr` -> `oinv_valR`
   + `valLr_inj_subproof` -> `valR_inj_subproof`
   + `valLr_surj_subproof` -> `valR_surj_subproof`
+- in `measure.v`:
+  + `measurable_bigcup` -> `bigcupT_measurable`
+  + `measurable_bigcap` -> `bigcapT_measurable`
+  + `measurable_bigcup_rat` -> `bigcupT_measurable_rat`
+- in `lebesgue_measure.v`:
+  + `emeasurable_bigcup` -> `bigcupT_emeasurable`
 
 ### Removed
 

theories/lebesgue_integral.v

@@ -929,7 +929,7 @@ apply: ereal_cvgrM => //; rewrite [X in _ --> X](_ : _ =
     mu (\bigcup_n (f @^-1` [set r] `&` fleg c n))); last first.
   by rewrite -setI_bigcupr bigcup_fleg// setIT.
 have ? k i : measurable (f @^-1` [set k] `&` fleg c i) by exact: measurableI.
-apply: cvg_mu_inc => //; first exact: measurable_bigcup.
+apply: cvg_mu_inc => //; first exact: bigcupT_measurable.
 move=> n m nm; apply/subsetPset; apply: setIS.
 by move/(nd_fleg c) : nm => /subsetPset.
 Unshelve. all: by end_near. Qed.
@@ -2874,7 +2874,7 @@ move=> mf; split=> [iDf0|Df0].
     apply/esym/cvg_lim => //; apply: cvg_mu_inc.
     - move=> i; apply: emeasurable_fun_c_infty => //.
       exact: measurable_fun_comp.
-    - apply: measurable_bigcup => i.
+    - apply: bigcupT_measurable => i.
       by apply: emeasurable_fun_c_infty => //; exact: measurable_fun_comp.
     - move=> m n mn; apply/subsetPset; apply: setIS => t /=.
       by apply: le_trans; rewrite lee_fin lef_pinv // ?ler_nat // posrE.
@@ -3491,11 +3491,11 @@ Let B := [set A | measurable A /\ measurable_fun setT (phi A)].
 Lemma xsection_ndseq_closed : ndseq_closed B.
 Proof.
 move=> F ndF; rewrite /B /= => BF; split.
-  by apply: measurable_bigcup => n; have [] := BF n.
+  by apply: bigcupT_measurable => n; have [] := BF n.
 have phiF x : (fun i => phi (F i) x) --> phi (\bigcup_i F i) x.
   rewrite /phi /= xsection_bigcup; apply: cvg_mu_inc => //.
   - by move=> n; apply: measurable_xsection; case: (BF n).
-  - by apply: measurable_bigcup => i; apply: measurable_xsection; case: (BF i).
+  - by apply: bigcupT_measurable => i; apply: measurable_xsection; case: (BF i).
   - move=> m n mn; apply/subsetPset => y; rewrite /xsection/= !inE.
     by have /subsetPset FmFn := ndF _ _ mn; exact: FmFn.
 apply: (emeasurable_fun_cvg (phi \o F)) => //.
@@ -3512,11 +3512,11 @@ Let B := [set A | measurable A /\ measurable_fun setT (psi A)].
 Lemma ysection_ndseq_closed : ndseq_closed B.
 Proof.
 move=> F ndF; rewrite /B /= => BF; split.
-  by apply: measurable_bigcup => n; have [] := BF n.
+  by apply: bigcupT_measurable => n; have [] := BF n.
 have psiF x : (fun i => psi (F i) x) --> psi (\bigcup_i F i) x.
   rewrite /psi /= ysection_bigcup; apply: cvg_mu_inc => //.
   - by move=> n; apply: measurable_ysection; case: (BF n).
-  - by apply: measurable_bigcup => i; apply: measurable_ysection; case: (BF i).
+  - by apply: bigcupT_measurable => i; apply: measurable_ysection; case: (BF i).
   - move=> m n mn; apply/subsetPset => y; rewrite /ysection/= !inE.
     by have /subsetPset FmFn := ndF _ _ mn; exact: FmFn.
 apply: (emeasurable_fun_cvg (psi \o F)) => //.