From b191831c0e45f57ca7e68d1e7319aa75cd71eedf Mon Sep 17 00:00:00 2001 From: Reynald Affeldt Date: Thu, 11 May 2023 23:06:47 +0900 Subject: [PATCH] sfinite -> sfinite_kernel (to match sfinite_measure) --- CHANGELOG_UNRELEASED.md | 4 ++-- theories/kernel.v | 22 ++++++++++------------ 2 files changed, 12 insertions(+), 14 deletions(-) diff --git a/CHANGELOG_UNRELEASED.md b/CHANGELOG_UNRELEASED.md index 6c58aa184..90ee2b186 100644 --- a/CHANGELOG_UNRELEASED.md +++ b/CHANGELOG_UNRELEASED.md @@ -29,8 +29,8 @@ `prob_pointed`, `mset`, `pset`, `pprobability`, `kprobability`, `kadd`, `mnormalize`, `knormalize`, `kcomp`, and `mkcomp`. + new lemmas `eq_kernel`, `measurable_fun_kseries`, `integral_kseries`, - `measure_fam_uubP`, `eq_sfkernel`, `kzero_uub`, `sfinite_finite`, - `sfinite`, `sfinite_kernel_measure`, `finite_kernel_measure`, + `measure_fam_uubP`, `eq_sfkernel`, `kzero_uub`, + `sfinite_kernel`, `sfinite_kernel_measure`, `finite_kernel_measure`, `measurable_prod_subset_xsection_kernel`, `measurable_fun_xsection_finite_kernel`, `measurable_fun_xsection_integral`, diff --git a/theories/kernel.v b/theories/kernel.v index 18f551682..76c1d3c46 100644 --- a/theories/kernel.v +++ b/theories/kernel.v @@ -160,17 +160,15 @@ End measure_fam_uub. HB.mixin Record Kernel_isSFinite_subdef d d' (X : measurableType d) (Y : measurableType d') (R : realType) (k : X -> {measure set Y -> \bar R}) := { - sfinite_subdef : exists2 s : (R.-ker X ~> Y)^nat, + sfinite_kernel_subdef : exists2 s : (R.-ker X ~> Y)^nat, forall n, measure_fam_uub (s n) & forall x U, measurable U -> k x U = kseries s x U }. -#[short(type=sfinite_kernel)] HB.structure Definition SFiniteKernel d d' (X : measurableType d) (Y : measurableType d') (R : realType) := { k of @Kernel _ _ _ _ R k & Kernel_isSFinite_subdef _ _ X Y R k }. -Notation "R .-sfker X ~> Y" := (sfinite_kernel X Y R). - -Arguments sfinite_subdef {_ _ _ _ _} _. +Notation "R .-sfker X ~> Y" := (SFiniteKernel.type X Y R). +Arguments sfinite_kernel_subdef {_ _ _ _ _} _. Lemma eq_sfkernel d d' (T : measurableType d) (T' : measurableType d') (R : realType) (k1 k2 : R.-sfker T ~> T') : @@ -221,7 +219,7 @@ End kzero. HB.builders Context d d' (X : measurableType d) (Y : measurableType d') (R : realType) k of Kernel_isFinite d d' X Y R k. -Lemma sfinite_finite : +Let sfinite_finite : exists2 k_ : (R.-ker _ ~> _)^nat, forall n, measure_fam_uub (k_ n) & forall x U, measurable U -> k x U = mseries (k_ ^~ x) 0 U. Proof. @@ -247,7 +245,7 @@ Context d d' (X : measurableType d) (Y : measurableType d'). Variables (R : realType) (k : R.-sfker X ~> Y). Let s : (X -> {measure set Y -> \bar R})^nat := - let: exist2 x _ _ := cid2 (sfinite_subdef k) in x. + let: exist2 x _ _ := cid2 (sfinite_kernel_subdef k) in x. Let ms n : @isKernel d d' X Y R (s n). Proof. @@ -262,7 +260,7 @@ Proof. by rewrite /s; case: cid2. Qed. HB.instance Definition _ n := @Kernel_isFinite.Build d d' X Y R (s n) (s_uub n). -Lemma sfinite : exists s : (R.-fker X ~> Y)^nat, +Lemma sfinite_kernel : exists s : (R.-fker X ~> Y)^nat, forall x U, measurable U -> k x U = kseries s x U. Proof. exists (fun n => [the _.-fker _ ~> _ of s n]) => x U mU. @@ -275,7 +273,7 @@ Lemma sfinite_kernel_measure d d' (Z : measurableType d) (X : measurableType d') (R : realType) (k : R.-sfker Z ~> X) (z : Z) : sfinite_measure (k z). Proof. -have [s ks] := sfinite k. +have [s ks] := sfinite_kernel k. exists (s ^~ z). move=> n; have [r snr] := measure_uub (s n). by apply: lty_fin_num_fun; rewrite (lt_le_trans (snr _))// leey. @@ -545,7 +543,7 @@ Lemma measurable_fun_integral_sfinite_kernel (l : R.-sfker X ~> Y) Proof. have [k_ [ndk_ k_k]] := approximation measurableT mk (fun xy _ => k0 xy). apply: (measurable_fun_xsection_integral ndk_ (k_k ^~ Logic.I)) => n r. -have [l_ hl_] := sfinite l. +have [l_ hl_] := sfinite_kernel l. rewrite (_ : (fun x => _) = (fun x => mseries (l_ ^~ x) 0 (xsection (k_ n @^-1` [set r]) x))); last first. by apply/funext => x; rewrite hl_//; exact/measurable_xsection. @@ -683,7 +681,7 @@ Let sfinite_kadd : exists2 k_ : (R.-ker _ ~> _)^nat, forall x U, measurable U -> kadd k1 k2 x U = mseries (k_ ^~ x) 0 U. Proof. -have [f1 hk1] := sfinite k1; have [f2 hk2] := sfinite k2. +have [f1 hk1] := sfinite_kernel k1; have [f2 hk2] := sfinite_kernel k2. exists (fun n => [the _.-ker _ ~> _ of kadd (f1 n) (f2 n)]). move=> n. have [r1 f1r1] := measure_uub (f1 n). @@ -954,7 +952,7 @@ Import KCOMP_FINITE_KERNEL. Lemma mkcomp_sfinite : exists k_ : (R.-fker X ~> Z)^nat, forall x U, measurable U -> (l \; k) x U = kseries k_ x U. Proof. -have [k_ hk_] := sfinite k; have [l_ hl_] := sfinite l. +have [k_ hk_] := sfinite_kernel k; have [l_ hl_] := sfinite_kernel l. have [kl hkl] : exists kl : (R.-fker X ~> Z) ^nat, forall x U, \esum_(i in setT) (l_ i.2 \; k_ i.1) x U = \sum_(i