measure_theory.function.conditional_expectation.unique
⟷
Mathlib.MeasureTheory.Function.ConditionalExpectation.Unique
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -48,8 +48,8 @@ section UniquenessOfConditionalExpectation
/-! ## Uniqueness of the conditional expectation -/
-#print MeasureTheory.lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero /-
-theorem lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero (hm : m ≤ m0) (f : lpMeas E' 𝕜 m p μ)
+#print MeasureTheory.lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero /-
+theorem lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero (hm : m ≤ m0) (f : lpMeas E' 𝕜 m p μ)
(hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞)
(hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
(hf_zero : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = 0) : f =ᵐ[μ] 0 :=
@@ -65,13 +65,13 @@ theorem lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero (hm : m ≤ m0) (f : lp
have hfg_restrict : f =ᵐ[μ.restrict s] g := ae_restrict_of_ae hfg
rw [integral_congr_ae hfg_restrict.symm]
exact hf_zero s hs hμs
-#align measure_theory.Lp_meas.ae_eq_zero_of_forall_set_integral_eq_zero MeasureTheory.lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero
+#align measure_theory.Lp_meas.ae_eq_zero_of_forall_set_integral_eq_zero MeasureTheory.lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero
-/
variable (𝕜)
-#print MeasureTheory.Lp.ae_eq_zero_of_forall_set_integral_eq_zero' /-
-theorem Lp.ae_eq_zero_of_forall_set_integral_eq_zero' (hm : m ≤ m0) (f : Lp E' p μ)
+#print MeasureTheory.Lp.ae_eq_zero_of_forall_setIntegral_eq_zero' /-
+theorem Lp.ae_eq_zero_of_forall_setIntegral_eq_zero' (hm : m ≤ m0) (f : Lp E' p μ)
(hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞)
(hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
(hf_zero : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = 0)
@@ -89,12 +89,12 @@ theorem Lp.ae_eq_zero_of_forall_set_integral_eq_zero' (hm : m ≤ m0) (f : Lp E'
have hfg_restrict : f =ᵐ[μ.restrict s] f_meas := ae_restrict_of_ae hf_f_meas
rw [integral_congr_ae hfg_restrict.symm]
exact hf_zero s hs hμs
-#align measure_theory.Lp.ae_eq_zero_of_forall_set_integral_eq_zero' MeasureTheory.Lp.ae_eq_zero_of_forall_set_integral_eq_zero'
+#align measure_theory.Lp.ae_eq_zero_of_forall_set_integral_eq_zero' MeasureTheory.Lp.ae_eq_zero_of_forall_setIntegral_eq_zero'
-/
-#print MeasureTheory.Lp.ae_eq_of_forall_set_integral_eq' /-
+#print MeasureTheory.Lp.ae_eq_of_forall_setIntegral_eq' /-
/-- **Uniqueness of the conditional expectation** -/
-theorem Lp.ae_eq_of_forall_set_integral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (hp_ne_zero : p ≠ 0)
+theorem Lp.ae_eq_of_forall_setIntegral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (hp_ne_zero : p ≠ 0)
(hp_ne_top : p ≠ ∞) (hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
(hg_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn g s μ)
(hfg : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ)
@@ -118,13 +118,13 @@ theorem Lp.ae_eq_of_forall_set_integral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (
exact
Lp.ae_eq_zero_of_forall_set_integral_eq_zero' 𝕜 hm (f - g) hp_ne_zero hp_ne_top hfg_int hfg'
hfg_meas
-#align measure_theory.Lp.ae_eq_of_forall_set_integral_eq' MeasureTheory.Lp.ae_eq_of_forall_set_integral_eq'
+#align measure_theory.Lp.ae_eq_of_forall_set_integral_eq' MeasureTheory.Lp.ae_eq_of_forall_setIntegral_eq'
-/
variable {𝕜}
-#print MeasureTheory.ae_eq_of_forall_set_integral_eq_of_sigmaFinite' /-
-theorem ae_eq_of_forall_set_integral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
+#print MeasureTheory.ae_eq_of_forall_setIntegral_eq_of_sigmaFinite' /-
+theorem ae_eq_of_forall_setIntegral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
{f g : α → F'} (hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
(hg_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn g s μ)
(hfg_eq : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ)
@@ -160,7 +160,7 @@ theorem ae_eq_of_forall_set_integral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFi
integral_congr_ae (ae_restrict_of_ae hgm.ae_eq_mk.symm)]
exact hfg_eq s hs hμs
exact ae_eq_of_forall_set_integral_eq_of_sigma_finite hf_mk_int_finite hg_mk_int_finite hfg_mk_eq
-#align measure_theory.ae_eq_of_forall_set_integral_eq_of_sigma_finite' MeasureTheory.ae_eq_of_forall_set_integral_eq_of_sigmaFinite'
+#align measure_theory.ae_eq_of_forall_set_integral_eq_of_sigma_finite' MeasureTheory.ae_eq_of_forall_setIntegral_eq_of_sigmaFinite'
-/
end UniquenessOfConditionalExpectation
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -3,8 +3,8 @@ Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
-import MeasureTheory.Function.AeEqOfIntegral
-import MeasureTheory.Function.ConditionalExpectation.AeMeasurable
+import MeasureTheory.Function.AEEqOfIntegral
+import MeasureTheory.Function.ConditionalExpectation.AEMeasurable
#align_import measure_theory.function.conditional_expectation.unique from "leanprover-community/mathlib"@"8af7091a43227e179939ba132e54e54e9f3b089a"
@@ -34,7 +34,7 @@ open scoped ENNReal MeasureTheory
namespace MeasureTheory
-variable {α E' F' 𝕜 : Type _} {p : ℝ≥0∞} {m m0 : MeasurableSpace α} {μ : Measure α} [IsROrC 𝕜]
+variable {α E' F' 𝕜 : Type _} {p : ℝ≥0∞} {m m0 : MeasurableSpace α} {μ : Measure α} [RCLike 𝕜]
-- 𝕜 for ℝ or ℂ
-- E' for an inner product space on which we compute integrals
[NormedAddCommGroup E']
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -135,7 +135,7 @@ theorem ae_eq_of_forall_set_integral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFi
∀ s, measurable_set[m] s → μ.trim hm s < ∞ → @integrable_on _ _ m _ (hfm.mk f) s (μ.trim hm) :=
by
intro s hs hμs
- rw [trim_measurable_set_eq hm hs] at hμs
+ rw [trim_measurable_set_eq hm hs] at hμs
rw [integrable_on, restrict_trim hm _ hs]
refine' integrable.trim hm _ hfm.strongly_measurable_mk
exact integrable.congr (hf_int_finite s hs hμs) (ae_restrict_of_ae hfm.ae_eq_mk)
@@ -143,7 +143,7 @@ theorem ae_eq_of_forall_set_integral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFi
∀ s, measurable_set[m] s → μ.trim hm s < ∞ → @integrable_on _ _ m _ (hgm.mk g) s (μ.trim hm) :=
by
intro s hs hμs
- rw [trim_measurable_set_eq hm hs] at hμs
+ rw [trim_measurable_set_eq hm hs] at hμs
rw [integrable_on, restrict_trim hm _ hs]
refine' integrable.trim hm _ hgm.strongly_measurable_mk
exact integrable.congr (hg_int_finite s hs hμs) (ae_restrict_of_ae hgm.ae_eq_mk)
@@ -153,7 +153,7 @@ theorem ae_eq_of_forall_set_integral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFi
μ.trim hm s < ∞ → ∫ x in s, hfm.mk f x ∂μ.trim hm = ∫ x in s, hgm.mk g x ∂μ.trim hm :=
by
intro s hs hμs
- rw [trim_measurable_set_eq hm hs] at hμs
+ rw [trim_measurable_set_eq hm hs] at hμs
rw [restrict_trim hm _ hs, ← integral_trim hm hfm.strongly_measurable_mk, ←
integral_trim hm hgm.strongly_measurable_mk,
integral_congr_ae (ae_restrict_of_ae hfm.ae_eq_mk.symm),
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
-import Mathbin.MeasureTheory.Function.AeEqOfIntegral
-import Mathbin.MeasureTheory.Function.ConditionalExpectation.AeMeasurable
+import MeasureTheory.Function.AeEqOfIntegral
+import MeasureTheory.Function.ConditionalExpectation.AeMeasurable
#align_import measure_theory.function.conditional_expectation.unique from "leanprover-community/mathlib"@"8af7091a43227e179939ba132e54e54e9f3b089a"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-
-! This file was ported from Lean 3 source module measure_theory.function.conditional_expectation.unique
-! leanprover-community/mathlib commit 8af7091a43227e179939ba132e54e54e9f3b089a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.MeasureTheory.Function.AeEqOfIntegral
import Mathbin.MeasureTheory.Function.ConditionalExpectation.AeMeasurable
+#align_import measure_theory.function.conditional_expectation.unique from "leanprover-community/mathlib"@"8af7091a43227e179939ba132e54e54e9f3b089a"
+
/-!
# Uniqueness of the conditional expectation
mathlib commit https://github.com/leanprover-community/mathlib/commit/bf9bbbcf0c1c1ead18280b0d010e417b10abb1b6
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
! This file was ported from Lean 3 source module measure_theory.function.conditional_expectation.unique
-! leanprover-community/mathlib commit d8bbb04e2d2a44596798a9207ceefc0fb236e41e
+! leanprover-community/mathlib commit 8af7091a43227e179939ba132e54e54e9f3b089a
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.MeasureTheory.Function.ConditionalExpectation.AeMeasurable
/-!
# Uniqueness of the conditional expectation
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
Two Lp functions `f, g` which are almost everywhere strongly measurable with respect to a σ-algebra
`m` and verify `∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ` for all `m`-measurable sets `s` are equal
almost everywhere. This proves the uniqueness of the conditional expectation, which is not yet
mathlib commit https://github.com/leanprover-community/mathlib/commit/8efcf8022aac8e01df8d302dcebdbc25d6a886c8
@@ -48,6 +48,7 @@ section UniquenessOfConditionalExpectation
/-! ## Uniqueness of the conditional expectation -/
+#print MeasureTheory.lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero /-
theorem lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero (hm : m ≤ m0) (f : lpMeas E' 𝕜 m p μ)
(hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞)
(hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
@@ -65,9 +66,11 @@ theorem lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero (hm : m ≤ m0) (f : lp
rw [integral_congr_ae hfg_restrict.symm]
exact hf_zero s hs hμs
#align measure_theory.Lp_meas.ae_eq_zero_of_forall_set_integral_eq_zero MeasureTheory.lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero
+-/
variable (𝕜)
+#print MeasureTheory.Lp.ae_eq_zero_of_forall_set_integral_eq_zero' /-
theorem Lp.ae_eq_zero_of_forall_set_integral_eq_zero' (hm : m ≤ m0) (f : Lp E' p μ)
(hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞)
(hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
@@ -87,7 +90,9 @@ theorem Lp.ae_eq_zero_of_forall_set_integral_eq_zero' (hm : m ≤ m0) (f : Lp E'
rw [integral_congr_ae hfg_restrict.symm]
exact hf_zero s hs hμs
#align measure_theory.Lp.ae_eq_zero_of_forall_set_integral_eq_zero' MeasureTheory.Lp.ae_eq_zero_of_forall_set_integral_eq_zero'
+-/
+#print MeasureTheory.Lp.ae_eq_of_forall_set_integral_eq' /-
/-- **Uniqueness of the conditional expectation** -/
theorem Lp.ae_eq_of_forall_set_integral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (hp_ne_zero : p ≠ 0)
(hp_ne_top : p ≠ ∞) (hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
@@ -114,10 +119,12 @@ theorem Lp.ae_eq_of_forall_set_integral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (
Lp.ae_eq_zero_of_forall_set_integral_eq_zero' 𝕜 hm (f - g) hp_ne_zero hp_ne_top hfg_int hfg'
hfg_meas
#align measure_theory.Lp.ae_eq_of_forall_set_integral_eq' MeasureTheory.Lp.ae_eq_of_forall_set_integral_eq'
+-/
variable {𝕜}
-theorem ae_eq_of_forall_set_integral_eq_of_sigma_finite' (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
+#print MeasureTheory.ae_eq_of_forall_set_integral_eq_of_sigmaFinite' /-
+theorem ae_eq_of_forall_set_integral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
{f g : α → F'} (hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
(hg_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn g s μ)
(hfg_eq : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ)
@@ -153,7 +160,8 @@ theorem ae_eq_of_forall_set_integral_eq_of_sigma_finite' (hm : m ≤ m0) [SigmaF
integral_congr_ae (ae_restrict_of_ae hgm.ae_eq_mk.symm)]
exact hfg_eq s hs hμs
exact ae_eq_of_forall_set_integral_eq_of_sigma_finite hf_mk_int_finite hg_mk_int_finite hfg_mk_eq
-#align measure_theory.ae_eq_of_forall_set_integral_eq_of_sigma_finite' MeasureTheory.ae_eq_of_forall_set_integral_eq_of_sigma_finite'
+#align measure_theory.ae_eq_of_forall_set_integral_eq_of_sigma_finite' MeasureTheory.ae_eq_of_forall_set_integral_eq_of_sigmaFinite'
+-/
end UniquenessOfConditionalExpectation
@@ -161,6 +169,7 @@ section IntegralNormLe
variable {s : Set α}
+#print MeasureTheory.integral_norm_le_of_forall_fin_meas_integral_eq /-
/-- Let `m` be a sub-σ-algebra of `m0`, `f` a `m0`-measurable function and `g` a `m`-measurable
function, such that their integrals coincide on `m`-measurable sets with finite measure.
Then `∫ x in s, ‖g x‖ ∂μ ≤ ∫ x in s, ‖f x‖ ∂μ` on all `m`-measurable sets with finite measure. -/
@@ -193,7 +202,9 @@ theorem integral_norm_le_of_forall_fin_meas_integral_eq (hm : m ≤ m0) {f g :
measure.restrict_restrict h_meas_nonpos_f]
exact set_integral_nonpos_le (hm _ h_meas_nonpos_g) hf hfi
#align measure_theory.integral_norm_le_of_forall_fin_meas_integral_eq MeasureTheory.integral_norm_le_of_forall_fin_meas_integral_eq
+-/
+#print MeasureTheory.lintegral_nnnorm_le_of_forall_fin_meas_integral_eq /-
/-- Let `m` be a sub-σ-algebra of `m0`, `f` a `m0`-measurable function and `g` a `m`-measurable
function, such that their integrals coincide on `m`-measurable sets with finite measure.
Then `∫⁻ x in s, ‖g x‖₊ ∂μ ≤ ∫⁻ x in s, ‖f x‖₊ ∂μ` on all `m`-measurable sets with finite
@@ -209,6 +220,7 @@ theorem lintegral_nnnorm_le_of_forall_fin_meas_integral_eq (hm : m ≤ m0) {f g
· exact integral_norm_le_of_forall_fin_meas_integral_eq hm hf hfi hg hgi hgf hs hμs
· exact integral_nonneg fun x => norm_nonneg _
#align measure_theory.lintegral_nnnorm_le_of_forall_fin_meas_integral_eq MeasureTheory.lintegral_nnnorm_le_of_forall_fin_meas_integral_eq
+-/
end IntegralNormLe
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -66,8 +66,6 @@ theorem lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero (hm : m ≤ m0) (f : lp
exact hf_zero s hs hμs
#align measure_theory.Lp_meas.ae_eq_zero_of_forall_set_integral_eq_zero MeasureTheory.lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero
-include 𝕜
-
variable (𝕜)
theorem Lp.ae_eq_zero_of_forall_set_integral_eq_zero' (hm : m ≤ m0) (f : Lp E' p μ)
@@ -119,8 +117,6 @@ theorem Lp.ae_eq_of_forall_set_integral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (
variable {𝕜}
-omit 𝕜
-
theorem ae_eq_of_forall_set_integral_eq_of_sigma_finite' (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
{f g : α → F'} (hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
(hg_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn g s μ)
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -74,7 +74,7 @@ theorem Lp.ae_eq_zero_of_forall_set_integral_eq_zero' (hm : m ≤ m0) (f : Lp E'
(hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞)
(hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
(hf_zero : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = 0)
- (hf_meas : AeStronglyMeasurable' m f μ) : f =ᵐ[μ] 0 :=
+ (hf_meas : AEStronglyMeasurable' m f μ) : f =ᵐ[μ] 0 :=
by
let f_meas : Lp_meas E' 𝕜 m p μ := ⟨f, hf_meas⟩
have hf_f_meas : f =ᵐ[μ] f_meas := by simp only [coeFn_coe_base', Subtype.coe_mk]
@@ -95,7 +95,7 @@ theorem Lp.ae_eq_of_forall_set_integral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (
(hp_ne_top : p ≠ ∞) (hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
(hg_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn g s μ)
(hfg : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ)
- (hf_meas : AeStronglyMeasurable' m f μ) (hg_meas : AeStronglyMeasurable' m g μ) : f =ᵐ[μ] g :=
+ (hf_meas : AEStronglyMeasurable' m f μ) (hg_meas : AEStronglyMeasurable' m g μ) : f =ᵐ[μ] g :=
by
suffices h_sub : ⇑(f - g) =ᵐ[μ] 0
· rw [← sub_ae_eq_zero]; exact (Lp.coe_fn_sub f g).symm.trans h_sub
@@ -125,7 +125,7 @@ theorem ae_eq_of_forall_set_integral_eq_of_sigma_finite' (hm : m ≤ m0) [SigmaF
{f g : α → F'} (hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
(hg_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn g s μ)
(hfg_eq : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ)
- (hfm : AeStronglyMeasurable' m f μ) (hgm : AeStronglyMeasurable' m g μ) : f =ᵐ[μ] g :=
+ (hfm : AEStronglyMeasurable' m f μ) (hgm : AEStronglyMeasurable' m g μ) : f =ᵐ[μ] g :=
by
rw [← ae_eq_trim_iff_of_ae_strongly_measurable' hm hfm hgm]
have hf_mk_int_finite :
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
set_integral
with setIntegral
(#12215)
Done with a global search and replace, and then (to fix the #align
lines), replace (#align \S*)setIntegral
with $1set_integral
.
@@ -19,9 +19,9 @@ defined in this file but is introduced in
## Main statements
-* `Lp.ae_eq_of_forall_set_integral_eq'`: two `Lp` functions verifying the equality of integrals
+* `Lp.ae_eq_of_forall_setIntegral_eq'`: two `Lp` functions verifying the equality of integrals
defining the conditional expectation are equal.
-* `ae_eq_of_forall_set_integral_eq_of_sigma_finite'`: two functions verifying the equality of
+* `ae_eq_of_forall_setIntegral_eq_of_sigma_finite'`: two functions verifying the equality of
integrals defining the conditional expectation are equal almost everywhere.
Requires `[SigmaFinite (μ.trim hm)]`.
@@ -46,7 +46,7 @@ section UniquenessOfConditionalExpectation
/-! ## Uniqueness of the conditional expectation -/
-theorem lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero (hm : m ≤ m0) (f : lpMeas E' 𝕜 m p μ)
+theorem lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero (hm : m ≤ m0) (f : lpMeas E' 𝕜 m p μ)
(hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞)
-- Porting note: needed to add explicit casts in the next two hypotheses
(hf_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn (f : Lp E' p μ) s μ)
@@ -56,7 +56,7 @@ theorem lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero (hm : m ≤ m0) (f : lp
refine' hfg.trans _
-- Porting note: added
unfold Filter.EventuallyEq at hfg
- refine' ae_eq_zero_of_forall_set_integral_eq_of_finStronglyMeasurable_trim hm _ _ hg_sm
+ refine' ae_eq_zero_of_forall_setIntegral_eq_of_finStronglyMeasurable_trim hm _ _ hg_sm
· intro s hs hμs
have hfg_restrict : f =ᵐ[μ.restrict s] g := ae_restrict_of_ae hfg
rw [IntegrableOn, integrable_congr hfg_restrict.symm]
@@ -65,11 +65,15 @@ theorem lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero (hm : m ≤ m0) (f : lp
have hfg_restrict : f =ᵐ[μ.restrict s] g := ae_restrict_of_ae hfg
rw [integral_congr_ae hfg_restrict.symm]
exact hf_zero s hs hμs
-#align measure_theory.Lp_meas.ae_eq_zero_of_forall_set_integral_eq_zero MeasureTheory.lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero
+#align measure_theory.Lp_meas.ae_eq_zero_of_forall_set_integral_eq_zero MeasureTheory.lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero
+
+@[deprecated]
+alias lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero :=
+ lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero -- deprecated on 2024-04-17
variable (𝕜)
-theorem Lp.ae_eq_zero_of_forall_set_integral_eq_zero' (hm : m ≤ m0) (f : Lp E' p μ)
+theorem Lp.ae_eq_zero_of_forall_setIntegral_eq_zero' (hm : m ≤ m0) (f : Lp E' p μ)
(hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞)
(hf_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn f s μ)
(hf_zero : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = 0)
@@ -78,7 +82,7 @@ theorem Lp.ae_eq_zero_of_forall_set_integral_eq_zero' (hm : m ≤ m0) (f : Lp E'
-- Porting note: `simp only` does not call `rfl` to try to close the goal. See https://github.com/leanprover-community/mathlib4/issues/5025
have hf_f_meas : f =ᵐ[μ] f_meas := by simp only [Subtype.coe_mk]; rfl
refine' hf_f_meas.trans _
- refine' lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero hm f_meas hp_ne_zero hp_ne_top _ _
+ refine' lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero hm f_meas hp_ne_zero hp_ne_top _ _
· intro s hs hμs
have hfg_restrict : f =ᵐ[μ.restrict s] f_meas := ae_restrict_of_ae hf_f_meas
rw [IntegrableOn, integrable_congr hfg_restrict.symm]
@@ -87,10 +91,14 @@ theorem Lp.ae_eq_zero_of_forall_set_integral_eq_zero' (hm : m ≤ m0) (f : Lp E'
have hfg_restrict : f =ᵐ[μ.restrict s] f_meas := ae_restrict_of_ae hf_f_meas
rw [integral_congr_ae hfg_restrict.symm]
exact hf_zero s hs hμs
-#align measure_theory.Lp.ae_eq_zero_of_forall_set_integral_eq_zero' MeasureTheory.Lp.ae_eq_zero_of_forall_set_integral_eq_zero'
+#align measure_theory.Lp.ae_eq_zero_of_forall_set_integral_eq_zero' MeasureTheory.Lp.ae_eq_zero_of_forall_setIntegral_eq_zero'
+
+@[deprecated]
+alias Lp.ae_eq_zero_of_forall_set_integral_eq_zero' :=
+ Lp.ae_eq_zero_of_forall_setIntegral_eq_zero' -- deprecated on 2024-04-17
/-- **Uniqueness of the conditional expectation** -/
-theorem Lp.ae_eq_of_forall_set_integral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (hp_ne_zero : p ≠ 0)
+theorem Lp.ae_eq_of_forall_setIntegral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (hp_ne_zero : p ≠ 0)
(hp_ne_top : p ≠ ∞) (hf_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn f s μ)
(hg_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn g s μ)
(hfg : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ)
@@ -110,13 +118,17 @@ theorem Lp.ae_eq_of_forall_set_integral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (
have hfg_meas : AEStronglyMeasurable' m (⇑(f - g)) μ :=
AEStronglyMeasurable'.congr (hf_meas.sub hg_meas) (Lp.coeFn_sub f g).symm
exact
- Lp.ae_eq_zero_of_forall_set_integral_eq_zero' 𝕜 hm (f - g) hp_ne_zero hp_ne_top hfg_int hfg'
+ Lp.ae_eq_zero_of_forall_setIntegral_eq_zero' 𝕜 hm (f - g) hp_ne_zero hp_ne_top hfg_int hfg'
hfg_meas
-#align measure_theory.Lp.ae_eq_of_forall_set_integral_eq' MeasureTheory.Lp.ae_eq_of_forall_set_integral_eq'
+#align measure_theory.Lp.ae_eq_of_forall_set_integral_eq' MeasureTheory.Lp.ae_eq_of_forall_setIntegral_eq'
+
+@[deprecated]
+alias Lp.ae_eq_of_forall_set_integral_eq' :=
+ Lp.ae_eq_of_forall_setIntegral_eq' -- deprecated on 2024-04-17
variable {𝕜}
-theorem ae_eq_of_forall_set_integral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
+theorem ae_eq_of_forall_setIntegral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
{f g : α → F'} (hf_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn f s μ)
(hg_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn g s μ)
(hfg_eq : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ)
@@ -155,8 +167,12 @@ theorem ae_eq_of_forall_set_integral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFi
integral_congr_ae (ae_restrict_of_ae hfm.ae_eq_mk.symm),
integral_congr_ae (ae_restrict_of_ae hgm.ae_eq_mk.symm)]
exact hfg_eq s hs hμs
- exact ae_eq_of_forall_set_integral_eq_of_sigmaFinite hf_mk_int_finite hg_mk_int_finite hfg_mk_eq
-#align measure_theory.ae_eq_of_forall_set_integral_eq_of_sigma_finite' MeasureTheory.ae_eq_of_forall_set_integral_eq_of_sigmaFinite'
+ exact ae_eq_of_forall_setIntegral_eq_of_sigmaFinite hf_mk_int_finite hg_mk_int_finite hfg_mk_eq
+#align measure_theory.ae_eq_of_forall_set_integral_eq_of_sigma_finite' MeasureTheory.ae_eq_of_forall_setIntegral_eq_of_sigmaFinite'
+
+@[deprecated]
+alias ae_eq_of_forall_set_integral_eq_of_sigmaFinite' :=
+ ae_eq_of_forall_setIntegral_eq_of_sigmaFinite' -- deprecated on 2024-04-17
end UniquenessOfConditionalExpectation
@@ -187,13 +203,13 @@ theorem integral_norm_le_of_forall_fin_meas_integral_eq (hm : m ≤ m0) {f g :
((measure_mono (Set.inter_subset_right _ _)).trans_lt (lt_top_iff_ne_top.mpr hμs)),
← Measure.restrict_restrict (hm _ h_meas_nonneg_g), ←
Measure.restrict_restrict h_meas_nonneg_f]
- exact set_integral_le_nonneg (hm _ h_meas_nonneg_g) hf hfi
+ exact setIntegral_le_nonneg (hm _ h_meas_nonneg_g) hf hfi
· rw [Measure.restrict_restrict (hm _ h_meas_nonpos_g), Measure.restrict_restrict h_meas_nonpos_f,
hgf _ (@MeasurableSet.inter α m _ _ h_meas_nonpos_g hs)
((measure_mono (Set.inter_subset_right _ _)).trans_lt (lt_top_iff_ne_top.mpr hμs)),
← Measure.restrict_restrict (hm _ h_meas_nonpos_g), ←
Measure.restrict_restrict h_meas_nonpos_f]
- exact set_integral_nonpos_le (hm _ h_meas_nonpos_g) hf hfi
+ exact setIntegral_nonpos_le (hm _ h_meas_nonpos_g) hf hfi
#align measure_theory.integral_norm_le_of_forall_fin_meas_integral_eq MeasureTheory.integral_norm_le_of_forall_fin_meas_integral_eq
/-- Let `m` be a sub-σ-algebra of `m0`, `f` an `m0`-measurable function and `g` an `m`-measurable
IsROrC
to RCLike
(#10819)
IsROrC
contains data, which goes against the expectation that classes prefixed with Is
are prop-valued. People have been complaining about this on and off, so this PR renames IsROrC
to RCLike
.
@@ -33,7 +33,7 @@ open scoped ENNReal MeasureTheory
namespace MeasureTheory
-variable {α E' F' 𝕜 : Type*} {p : ℝ≥0∞} {m m0 : MeasurableSpace α} {μ : Measure α} [IsROrC 𝕜]
+variable {α E' F' 𝕜 : Type*} {p : ℝ≥0∞} {m m0 : MeasurableSpace α} {μ : Measure α} [RCLike 𝕜]
-- 𝕜 for ℝ or ℂ
-- E' for an inner product space on which we compute integrals
[NormedAddCommGroup E']
@@ -208,7 +208,7 @@ theorem lintegral_nnnorm_le_of_forall_fin_meas_integral_eq (hm : m ≤ m0) {f g
rw [← ofReal_integral_norm_eq_lintegral_nnnorm hfi, ←
ofReal_integral_norm_eq_lintegral_nnnorm hgi, ENNReal.ofReal_le_ofReal_iff]
· exact integral_norm_le_of_forall_fin_meas_integral_eq hm hf hfi hg hgi hgf hs hμs
- · exact integral_nonneg fun x => norm_nonneg _
+ · positivity
#align measure_theory.lintegral_nnnorm_le_of_forall_fin_meas_integral_eq MeasureTheory.lintegral_nnnorm_le_of_forall_fin_meas_integral_eq
end IntegralNormLE
have
, replace
and suffices
(#10640)
No changes to tactic file, it's just boring fixes throughout the library.
This follows on from #6964.
Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
@@ -96,8 +96,8 @@ theorem Lp.ae_eq_of_forall_set_integral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (
(hfg : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ)
(hf_meas : AEStronglyMeasurable' m f μ) (hg_meas : AEStronglyMeasurable' m g μ) :
f =ᵐ[μ] g := by
- suffices h_sub : ⇑(f - g) =ᵐ[μ] 0
- · rw [← sub_ae_eq_zero]; exact (Lp.coeFn_sub f g).symm.trans h_sub
+ suffices h_sub : ⇑(f - g) =ᵐ[μ] 0 by
+ rw [← sub_ae_eq_zero]; exact (Lp.coeFn_sub f g).symm.trans h_sub
have hfg' : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → (∫ x in s, (f - g) x ∂μ) = 0 := by
intro s hs hμs
rw [integral_congr_ae (ae_restrict_of_ae (Lp.coeFn_sub f g))]
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -33,7 +33,7 @@ open scoped ENNReal MeasureTheory
namespace MeasureTheory
-variable {α E' F' 𝕜 : Type _} {p : ℝ≥0∞} {m m0 : MeasurableSpace α} {μ : Measure α} [IsROrC 𝕜]
+variable {α E' F' 𝕜 : Type*} {p : ℝ≥0∞} {m m0 : MeasurableSpace α} {μ : Measure α} [IsROrC 𝕜]
-- 𝕜 for ℝ or ℂ
-- E' for an inner product space on which we compute integrals
[NormedAddCommGroup E']
@@ -2,15 +2,12 @@
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-
-! This file was ported from Lean 3 source module measure_theory.function.conditional_expectation.unique
-! leanprover-community/mathlib commit d8bbb04e2d2a44596798a9207ceefc0fb236e41e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.MeasureTheory.Function.AEEqOfIntegral
import Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable
+#align_import measure_theory.function.conditional_expectation.unique from "leanprover-community/mathlib"@"d8bbb04e2d2a44596798a9207ceefc0fb236e41e"
+
/-!
# Uniqueness of the conditional expectation
@@ -167,7 +167,7 @@ section IntegralNormLE
variable {s : Set α}
-/-- Let `m` be a sub-σ-algebra of `m0`, `f` a `m0`-measurable function and `g` a `m`-measurable
+/-- Let `m` be a sub-σ-algebra of `m0`, `f` an `m0`-measurable function and `g` an `m`-measurable
function, such that their integrals coincide on `m`-measurable sets with finite measure.
Then `∫ x in s, ‖g x‖ ∂μ ≤ ∫ x in s, ‖f x‖ ∂μ` on all `m`-measurable sets with finite measure. -/
theorem integral_norm_le_of_forall_fin_meas_integral_eq (hm : m ≤ m0) {f g : α → ℝ}
@@ -199,7 +199,7 @@ theorem integral_norm_le_of_forall_fin_meas_integral_eq (hm : m ≤ m0) {f g :
exact set_integral_nonpos_le (hm _ h_meas_nonpos_g) hf hfi
#align measure_theory.integral_norm_le_of_forall_fin_meas_integral_eq MeasureTheory.integral_norm_le_of_forall_fin_meas_integral_eq
-/-- Let `m` be a sub-σ-algebra of `m0`, `f` a `m0`-measurable function and `g` a `m`-measurable
+/-- Let `m` be a sub-σ-algebra of `m0`, `f` an `m0`-measurable function and `g` an `m`-measurable
function, such that their integrals coincide on `m`-measurable sets with finite measure.
Then `∫⁻ x in s, ‖g x‖₊ ∂μ ≤ ∫⁻ x in s, ‖f x‖₊ ∂μ` on all `m`-measurable sets with finite
measure. -/
@@ -75,7 +75,7 @@ variable (𝕜)
theorem Lp.ae_eq_zero_of_forall_set_integral_eq_zero' (hm : m ≤ m0) (f : Lp E' p μ)
(hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞)
(hf_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn f s μ)
- (hf_zero : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → (∫ x in s, f x ∂μ) = 0)
+ (hf_zero : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = 0)
(hf_meas : AEStronglyMeasurable' m f μ) : f =ᵐ[μ] 0 := by
let f_meas : lpMeas E' 𝕜 m p μ := ⟨f, hf_meas⟩
-- Porting note: `simp only` does not call `rfl` to try to close the goal. See https://github.com/leanprover-community/mathlib4/issues/5025
@@ -96,7 +96,7 @@ theorem Lp.ae_eq_zero_of_forall_set_integral_eq_zero' (hm : m ≤ m0) (f : Lp E'
theorem Lp.ae_eq_of_forall_set_integral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (hp_ne_zero : p ≠ 0)
(hp_ne_top : p ≠ ∞) (hf_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn f s μ)
(hg_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn g s μ)
- (hfg : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → (∫ x in s, f x ∂μ) = ∫ x in s, g x ∂μ)
+ (hfg : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ)
(hf_meas : AEStronglyMeasurable' m f μ) (hg_meas : AEStronglyMeasurable' m g μ) :
f =ᵐ[μ] g := by
suffices h_sub : ⇑(f - g) =ᵐ[μ] 0
@@ -122,7 +122,7 @@ variable {𝕜}
theorem ae_eq_of_forall_set_integral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
{f g : α → F'} (hf_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn f s μ)
(hg_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn g s μ)
- (hfg_eq : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → (∫ x in s, f x ∂μ) = ∫ x in s, g x ∂μ)
+ (hfg_eq : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ)
(hfm : AEStronglyMeasurable' m f μ) (hgm : AEStronglyMeasurable' m g μ) : f =ᵐ[μ] g := by
rw [← ae_eq_trim_iff_of_aeStronglyMeasurable' hm hfm hgm]
have hf_mk_int_finite :
@@ -150,7 +150,7 @@ theorem ae_eq_of_forall_set_integral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFi
have hfg_mk_eq :
∀ s : Set α,
MeasurableSet[m] s →
- μ.trim hm s < ∞ → (∫ x in s, hfm.mk f x ∂μ.trim hm) = ∫ x in s, hgm.mk g x ∂μ.trim hm := by
+ μ.trim hm s < ∞ → ∫ x in s, hfm.mk f x ∂μ.trim hm = ∫ x in s, hgm.mk g x ∂μ.trim hm := by
intro s hs hμs
rw [trim_measurableSet_eq hm hs] at hμs
rw [restrict_trim hm _ hs, ← integral_trim hm hfm.stronglyMeasurable_mk, ←
@@ -173,7 +173,7 @@ Then `∫ x in s, ‖g x‖ ∂μ ≤ ∫ x in s, ‖f x‖ ∂μ` on all `m`-me
theorem integral_norm_le_of_forall_fin_meas_integral_eq (hm : m ≤ m0) {f g : α → ℝ}
(hf : StronglyMeasurable f) (hfi : IntegrableOn f s μ) (hg : StronglyMeasurable[m] g)
(hgi : IntegrableOn g s μ)
- (hgf : ∀ t, MeasurableSet[m] t → μ t < ∞ → (∫ x in t, g x ∂μ) = ∫ x in t, f x ∂μ)
+ (hgf : ∀ t, MeasurableSet[m] t → μ t < ∞ → ∫ x in t, g x ∂μ = ∫ x in t, f x ∂μ)
(hs : MeasurableSet[m] s) (hμs : μ s ≠ ∞) : (∫ x in s, ‖g x‖ ∂μ) ≤ ∫ x in s, ‖f x‖ ∂μ := by
rw [integral_norm_eq_pos_sub_neg hgi, integral_norm_eq_pos_sub_neg hfi]
have h_meas_nonneg_g : MeasurableSet[m] {x | 0 ≤ g x} :=
@@ -206,7 +206,7 @@ measure. -/
theorem lintegral_nnnorm_le_of_forall_fin_meas_integral_eq (hm : m ≤ m0) {f g : α → ℝ}
(hf : StronglyMeasurable f) (hfi : IntegrableOn f s μ) (hg : StronglyMeasurable[m] g)
(hgi : IntegrableOn g s μ)
- (hgf : ∀ t, MeasurableSet[m] t → μ t < ∞ → (∫ x in t, g x ∂μ) = ∫ x in t, f x ∂μ)
+ (hgf : ∀ t, MeasurableSet[m] t → μ t < ∞ → ∫ x in t, g x ∂μ = ∫ x in t, f x ∂μ)
(hs : MeasurableSet[m] s) (hμs : μ s ≠ ∞) : (∫⁻ x in s, ‖g x‖₊ ∂μ) ≤ ∫⁻ x in s, ‖f x‖₊ ∂μ := by
rw [← ofReal_integral_norm_eq_lintegral_nnnorm hfi, ←
ofReal_integral_norm_eq_lintegral_nnnorm hgi, ENNReal.ofReal_le_ofReal_iff]
The unported dependencies are
algebra.order.module
init.core
linear_algebra.free_module.finite.rank
algebra.order.monoid.cancel.defs
algebra.abs
algebra.group_power.lemmas
init.data.list.basic
linear_algebra.free_module.rank
algebra.order.monoid.cancel.basic
init.data.list.default
topology.subset_properties
init.logic
The following 1 dependencies have changed in mathlib3 since they were ported, which may complicate porting this file