measure_theory.function.lp_order
⟷
Mathlib.MeasureTheory.Function.LpOrder
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
@@ -123,11 +123,11 @@ noncomputable instance [Fact (1 ≤ p)] : NormedLatticeAddCommGroup (Lp E p μ)
Lp.instNormedAddCommGroup with
add_le_add_left := fun f g => add_le_add_left
solid := fun f g hfg => by
- rw [← coe_fn_le] at hfg
+ rw [← coe_fn_le] at hfg
simp_rw [Lp.norm_def, ENNReal.toReal_le_toReal (Lp.snorm_ne_top f) (Lp.snorm_ne_top g)]
refine' snorm_mono_ae _
filter_upwards [hfg, Lp.coe_fn_abs f, Lp.coe_fn_abs g] with x hx hxf hxg
- rw [hxf, hxg] at hx
+ rw [hxf, hxg] at hx
exact HasSolidNorm.solid hx }
end Order
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.Analysis.Normed.Order.Lattice
-import Mathbin.MeasureTheory.Function.LpSpace
+import Analysis.Normed.Order.Lattice
+import MeasureTheory.Function.LpSpace
#align_import measure_theory.function.lp_order from "leanprover-community/mathlib"@"f60c6087a7275b72d5db3c5a1d0e19e35a429c0a"
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.lp_order
-! leanprover-community/mathlib commit f60c6087a7275b72d5db3c5a1d0e19e35a429c0a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Analysis.Normed.Order.Lattice
import Mathbin.MeasureTheory.Function.LpSpace
+#align_import measure_theory.function.lp_order from "leanprover-community/mathlib"@"f60c6087a7275b72d5db3c5a1d0e19e35a429c0a"
+
/-!
# Order related properties of Lp spaces
mathlib commit https://github.com/leanprover-community/mathlib/commit/9240e8be927a0955b9a82c6c85ef499ee3a626b8
@@ -89,7 +89,7 @@ theorem MeasureTheory.Memℒp.inf {f g : α → E} (hf : Memℒp f p μ) (hg : M
-/
#print MeasureTheory.Memℒp.abs /-
-theorem MeasureTheory.Memℒp.abs {f : α → E} (hf : Memℒp f p μ) : Memℒp (|f|) p μ :=
+theorem MeasureTheory.Memℒp.abs {f : α → E} (hf : Memℒp f p μ) : Memℒp |f| p μ :=
hf.sup hf.neg
#align measure_theory.mem_ℒp.abs MeasureTheory.Memℒp.abs
-/
@@ -116,7 +116,7 @@ theorem coeFn_inf (f g : Lp E p μ) : ⇑(f ⊓ g) =ᵐ[μ] ⇑f ⊓ ⇑g :=
-/
#print MeasureTheory.Lp.coeFn_abs /-
-theorem coeFn_abs (f : Lp E p μ) : ⇑(|f|) =ᵐ[μ] fun x => |f x| :=
+theorem coeFn_abs (f : Lp E p μ) : ⇑|f| =ᵐ[μ] fun x => |f x| :=
AEEqFun.coeFn_abs _
#align measure_theory.Lp.coe_fn_abs MeasureTheory.Lp.coeFn_abs
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -43,10 +43,13 @@ section Order
variable [NormedLatticeAddCommGroup E]
+#print MeasureTheory.Lp.coeFn_le /-
theorem coeFn_le (f g : Lp E p μ) : f ≤ᵐ[μ] g ↔ f ≤ g := by
rw [← Subtype.coe_le_coe, ← ae_eq_fun.coe_fn_le, ← coeFn_coeBase, ← coeFn_coeBase]
#align measure_theory.Lp.coe_fn_le MeasureTheory.Lp.coeFn_le
+-/
+#print MeasureTheory.Lp.coeFn_nonneg /-
theorem coeFn_nonneg (f : Lp E p μ) : 0 ≤ᵐ[μ] f ↔ 0 ≤ f :=
by
rw [← coe_fn_le]
@@ -55,6 +58,7 @@ theorem coeFn_nonneg (f : Lp E p μ) : 0 ≤ᵐ[μ] f ↔ 0 ≤ f :=
· rwa [h2]
· rwa [← h2]
#align measure_theory.Lp.coe_fn_nonneg MeasureTheory.Lp.coeFn_nonneg
+-/
instance : CovariantClass (Lp E p μ) (Lp E p μ) (· + ·) (· ≤ ·) :=
by
@@ -68,21 +72,27 @@ instance : OrderedAddCommGroup (Lp E p μ) :=
{ Subtype.partialOrder _, AddSubgroup.toAddCommGroup _ with
add_le_add_left := fun f g => add_le_add_left }
+#print MeasureTheory.Memℒp.sup /-
theorem MeasureTheory.Memℒp.sup {f g : α → E} (hf : Memℒp f p μ) (hg : Memℒp g p μ) :
Memℒp (f ⊔ g) p μ :=
Memℒp.mono' (hf.norm.add hg.norm) (hf.1.sup hg.1)
(Filter.eventually_of_forall fun x => norm_sup_le_add (f x) (g x))
#align measure_theory.mem_ℒp.sup MeasureTheory.Memℒp.sup
+-/
+#print MeasureTheory.Memℒp.inf /-
theorem MeasureTheory.Memℒp.inf {f g : α → E} (hf : Memℒp f p μ) (hg : Memℒp g p μ) :
Memℒp (f ⊓ g) p μ :=
Memℒp.mono' (hf.norm.add hg.norm) (hf.1.inf hg.1)
(Filter.eventually_of_forall fun x => norm_inf_le_add (f x) (g x))
#align measure_theory.mem_ℒp.inf MeasureTheory.Memℒp.inf
+-/
+#print MeasureTheory.Memℒp.abs /-
theorem MeasureTheory.Memℒp.abs {f : α → E} (hf : Memℒp f p μ) : Memℒp (|f|) p μ :=
hf.sup hf.neg
#align measure_theory.mem_ℒp.abs MeasureTheory.Memℒp.abs
+-/
instance : Lattice (Lp E p μ) :=
Subtype.lattice
@@ -93,17 +103,23 @@ instance : Lattice (Lp E p μ) :=
rw [mem_Lp_iff_mem_ℒp] at *
exact (mem_ℒp_congr_ae (ae_eq_fun.coe_fn_inf _ _)).mpr (hf.inf hg)
+#print MeasureTheory.Lp.coeFn_sup /-
theorem coeFn_sup (f g : Lp E p μ) : ⇑(f ⊔ g) =ᵐ[μ] ⇑f ⊔ ⇑g :=
AEEqFun.coeFn_sup _ _
#align measure_theory.Lp.coe_fn_sup MeasureTheory.Lp.coeFn_sup
+-/
+#print MeasureTheory.Lp.coeFn_inf /-
theorem coeFn_inf (f g : Lp E p μ) : ⇑(f ⊓ g) =ᵐ[μ] ⇑f ⊓ ⇑g :=
AEEqFun.coeFn_inf _ _
#align measure_theory.Lp.coe_fn_inf MeasureTheory.Lp.coeFn_inf
+-/
+#print MeasureTheory.Lp.coeFn_abs /-
theorem coeFn_abs (f : Lp E p μ) : ⇑(|f|) =ᵐ[μ] fun x => |f x| :=
AEEqFun.coeFn_abs _
#align measure_theory.Lp.coe_fn_abs MeasureTheory.Lp.coeFn_abs
+-/
noncomputable instance [Fact (1 ≤ p)] : NormedLatticeAddCommGroup (Lp E p μ) :=
{ Lp.instLattice,
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -51,7 +51,7 @@ theorem coeFn_nonneg (f : Lp E p μ) : 0 ≤ᵐ[μ] f ↔ 0 ≤ f :=
by
rw [← coe_fn_le]
have h0 := Lp.coe_fn_zero E p μ
- constructor <;> intro h <;> filter_upwards [h, h0]with _ _ h2
+ constructor <;> intro h <;> filter_upwards [h, h0] with _ _ h2
· rwa [h2]
· rwa [← h2]
#align measure_theory.Lp.coe_fn_nonneg MeasureTheory.Lp.coeFn_nonneg
@@ -60,7 +60,7 @@ instance : CovariantClass (Lp E p μ) (Lp E p μ) (· + ·) (· ≤ ·) :=
by
refine' ⟨fun f g₁ g₂ hg₁₂ => _⟩
rw [← coe_fn_le] at hg₁₂ ⊢
- filter_upwards [coe_fn_add f g₁, coe_fn_add f g₂, hg₁₂]with _ h1 h2 h3
+ filter_upwards [coe_fn_add f g₁, coe_fn_add f g₂, hg₁₂] with _ h1 h2 h3
rw [h1, h2, Pi.add_apply, Pi.add_apply]
exact add_le_add le_rfl h3
@@ -113,7 +113,7 @@ noncomputable instance [Fact (1 ≤ p)] : NormedLatticeAddCommGroup (Lp E p μ)
rw [← coe_fn_le] at hfg
simp_rw [Lp.norm_def, ENNReal.toReal_le_toReal (Lp.snorm_ne_top f) (Lp.snorm_ne_top g)]
refine' snorm_mono_ae _
- filter_upwards [hfg, Lp.coe_fn_abs f, Lp.coe_fn_abs g]with x hx hxf hxg
+ filter_upwards [hfg, Lp.coe_fn_abs f, Lp.coe_fn_abs g] with x hx hxf hxg
rw [hxf, hxg] at hx
exact HasSolidNorm.solid hx }
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -59,7 +59,7 @@ theorem coeFn_nonneg (f : Lp E p μ) : 0 ≤ᵐ[μ] f ↔ 0 ≤ f :=
instance : CovariantClass (Lp E p μ) (Lp E p μ) (· + ·) (· ≤ ·) :=
by
refine' ⟨fun f g₁ g₂ hg₁₂ => _⟩
- rw [← coe_fn_le] at hg₁₂⊢
+ rw [← coe_fn_le] at hg₁₂ ⊢
filter_upwards [coe_fn_add f g₁, coe_fn_add f g₂, hg₁₂]with _ h1 h2 h3
rw [h1, h2, Pi.add_apply, Pi.add_apply]
exact add_le_add le_rfl h3
@@ -110,11 +110,11 @@ noncomputable instance [Fact (1 ≤ p)] : NormedLatticeAddCommGroup (Lp E p μ)
Lp.instNormedAddCommGroup with
add_le_add_left := fun f g => add_le_add_left
solid := fun f g hfg => by
- rw [← coe_fn_le] at hfg
+ rw [← coe_fn_le] at hfg
simp_rw [Lp.norm_def, ENNReal.toReal_le_toReal (Lp.snorm_ne_top f) (Lp.snorm_ne_top g)]
refine' snorm_mono_ae _
filter_upwards [hfg, Lp.coe_fn_abs f, Lp.coe_fn_abs g]with x hx hxf hxg
- rw [hxf, hxg] at hx
+ rw [hxf, hxg] at hx
exact HasSolidNorm.solid hx }
end Order
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -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.lp_order
-! leanprover-community/mathlib commit 5dc275ec639221ca4d5f56938eb966f6ad9bc89f
+! leanprover-community/mathlib commit f60c6087a7275b72d5db3c5a1d0e19e35a429c0a
! 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.LpSpace
/-!
# Order related properties of Lp spaces
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
### Results
- `Lp E p μ` is an `ordered_add_comm_group` when `E` is a `normed_lattice_add_comm_group`.
@@ -40,20 +43,20 @@ section Order
variable [NormedLatticeAddCommGroup E]
-theorem coeFn_le (f g : lp E p μ) : f ≤ᵐ[μ] g ↔ f ≤ g := by
+theorem coeFn_le (f g : Lp E p μ) : f ≤ᵐ[μ] g ↔ f ≤ g := by
rw [← Subtype.coe_le_coe, ← ae_eq_fun.coe_fn_le, ← coeFn_coeBase, ← coeFn_coeBase]
-#align measure_theory.Lp.coe_fn_le MeasureTheory.lp.coeFn_le
+#align measure_theory.Lp.coe_fn_le MeasureTheory.Lp.coeFn_le
-theorem coeFn_nonneg (f : lp E p μ) : 0 ≤ᵐ[μ] f ↔ 0 ≤ f :=
+theorem coeFn_nonneg (f : Lp E p μ) : 0 ≤ᵐ[μ] f ↔ 0 ≤ f :=
by
rw [← coe_fn_le]
have h0 := Lp.coe_fn_zero E p μ
constructor <;> intro h <;> filter_upwards [h, h0]with _ _ h2
· rwa [h2]
· rwa [← h2]
-#align measure_theory.Lp.coe_fn_nonneg MeasureTheory.lp.coeFn_nonneg
+#align measure_theory.Lp.coe_fn_nonneg MeasureTheory.Lp.coeFn_nonneg
-instance : CovariantClass (lp E p μ) (lp E p μ) (· + ·) (· ≤ ·) :=
+instance : CovariantClass (Lp E p μ) (Lp E p μ) (· + ·) (· ≤ ·) :=
by
refine' ⟨fun f g₁ g₂ hg₁₂ => _⟩
rw [← coe_fn_le] at hg₁₂⊢
@@ -61,7 +64,7 @@ instance : CovariantClass (lp E p μ) (lp E p μ) (· + ·) (· ≤ ·) :=
rw [h1, h2, Pi.add_apply, Pi.add_apply]
exact add_le_add le_rfl h3
-instance : OrderedAddCommGroup (lp E p μ) :=
+instance : OrderedAddCommGroup (Lp E p μ) :=
{ Subtype.partialOrder _, AddSubgroup.toAddCommGroup _ with
add_le_add_left := fun f g => add_le_add_left }
@@ -81,7 +84,7 @@ theorem MeasureTheory.Memℒp.abs {f : α → E} (hf : Memℒp f p μ) : Memℒp
hf.sup hf.neg
#align measure_theory.mem_ℒp.abs MeasureTheory.Memℒp.abs
-instance : Lattice (lp E p μ) :=
+instance : Lattice (Lp E p μ) :=
Subtype.lattice
(fun f g hf hg => by
rw [mem_Lp_iff_mem_ℒp] at *
@@ -90,21 +93,21 @@ instance : Lattice (lp E p μ) :=
rw [mem_Lp_iff_mem_ℒp] at *
exact (mem_ℒp_congr_ae (ae_eq_fun.coe_fn_inf _ _)).mpr (hf.inf hg)
-theorem coeFn_sup (f g : lp E p μ) : ⇑(f ⊔ g) =ᵐ[μ] ⇑f ⊔ ⇑g :=
+theorem coeFn_sup (f g : Lp E p μ) : ⇑(f ⊔ g) =ᵐ[μ] ⇑f ⊔ ⇑g :=
AEEqFun.coeFn_sup _ _
-#align measure_theory.Lp.coe_fn_sup MeasureTheory.lp.coeFn_sup
+#align measure_theory.Lp.coe_fn_sup MeasureTheory.Lp.coeFn_sup
-theorem coeFn_inf (f g : lp E p μ) : ⇑(f ⊓ g) =ᵐ[μ] ⇑f ⊓ ⇑g :=
+theorem coeFn_inf (f g : Lp E p μ) : ⇑(f ⊓ g) =ᵐ[μ] ⇑f ⊓ ⇑g :=
AEEqFun.coeFn_inf _ _
-#align measure_theory.Lp.coe_fn_inf MeasureTheory.lp.coeFn_inf
+#align measure_theory.Lp.coe_fn_inf MeasureTheory.Lp.coeFn_inf
-theorem coeFn_abs (f : lp E p μ) : ⇑(|f|) =ᵐ[μ] fun x => |f x| :=
+theorem coeFn_abs (f : Lp E p μ) : ⇑(|f|) =ᵐ[μ] fun x => |f x| :=
AEEqFun.coeFn_abs _
-#align measure_theory.Lp.coe_fn_abs MeasureTheory.lp.coeFn_abs
+#align measure_theory.Lp.coe_fn_abs MeasureTheory.Lp.coeFn_abs
-noncomputable instance [Fact (1 ≤ p)] : NormedLatticeAddCommGroup (lp E p μ) :=
- { lp.lattice,
- lp.normedAddCommGroup with
+noncomputable instance [Fact (1 ≤ p)] : NormedLatticeAddCommGroup (Lp E p μ) :=
+ { Lp.instLattice,
+ Lp.instNormedAddCommGroup with
add_le_add_left := fun f g => add_le_add_left
solid := fun f g hfg => by
rw [← coe_fn_le] at hfg
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -28,7 +28,7 @@ import Mathbin.MeasureTheory.Function.LpSpace
open TopologicalSpace MeasureTheory LatticeOrderedCommGroup
-open ENNReal
+open scoped ENNReal
variable {α E : Type _} {m : MeasurableSpace α} {μ : Measure α} {p : ℝ≥0∞}
mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b
@@ -91,15 +91,15 @@ instance : Lattice (lp E p μ) :=
exact (mem_ℒp_congr_ae (ae_eq_fun.coe_fn_inf _ _)).mpr (hf.inf hg)
theorem coeFn_sup (f g : lp E p μ) : ⇑(f ⊔ g) =ᵐ[μ] ⇑f ⊔ ⇑g :=
- AeEqFun.coeFn_sup _ _
+ AEEqFun.coeFn_sup _ _
#align measure_theory.Lp.coe_fn_sup MeasureTheory.lp.coeFn_sup
theorem coeFn_inf (f g : lp E p μ) : ⇑(f ⊓ g) =ᵐ[μ] ⇑f ⊓ ⇑g :=
- AeEqFun.coeFn_inf _ _
+ AEEqFun.coeFn_inf _ _
#align measure_theory.Lp.coe_fn_inf MeasureTheory.lp.coeFn_inf
theorem coeFn_abs (f : lp E p μ) : ⇑(|f|) =ᵐ[μ] fun x => |f x| :=
- AeEqFun.coeFn_abs _
+ AEEqFun.coeFn_abs _
#align measure_theory.Lp.coe_fn_abs MeasureTheory.lp.coeFn_abs
noncomputable instance [Fact (1 ≤ p)] : NormedLatticeAddCommGroup (lp E p μ) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740
@@ -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.lp_order
-! leanprover-community/mathlib commit 7f5bf383ec988aa0ea700583c6449332003722a7
+! leanprover-community/mathlib commit 5dc275ec639221ca4d5f56938eb966f6ad9bc89f
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -112,7 +112,7 @@ noncomputable instance [Fact (1 ≤ p)] : NormedLatticeAddCommGroup (lp E p μ)
refine' snorm_mono_ae _
filter_upwards [hfg, Lp.coe_fn_abs f, Lp.coe_fn_abs g]with x hx hxf hxg
rw [hxf, hxg] at hx
- exact solid hx }
+ exact HasSolidNorm.solid hx }
end Order
mathlib commit https://github.com/leanprover-community/mathlib/commit/28b2a92f2996d28e580450863c130955de0ed398
@@ -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.lp_order
-! leanprover-community/mathlib commit 5dc275ec639221ca4d5f56938eb966f6ad9bc89f
+! leanprover-community/mathlib commit 7f5bf383ec988aa0ea700583c6449332003722a7
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -112,7 +112,7 @@ noncomputable instance [Fact (1 ≤ p)] : NormedLatticeAddCommGroup (lp E p μ)
refine' snorm_mono_ae _
filter_upwards [hfg, Lp.coe_fn_abs f, Lp.coe_fn_abs g]with x hx hxf hxg
rw [hxf, hxg] at hx
- exact HasSolidNorm.solid hx }
+ exact solid hx }
end Order
mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740
@@ -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.lp_order
-! leanprover-community/mathlib commit 7f5bf383ec988aa0ea700583c6449332003722a7
+! leanprover-community/mathlib commit 5dc275ec639221ca4d5f56938eb966f6ad9bc89f
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -112,7 +112,7 @@ noncomputable instance [Fact (1 ≤ p)] : NormedLatticeAddCommGroup (lp E p μ)
refine' snorm_mono_ae _
filter_upwards [hfg, Lp.coe_fn_abs f, Lp.coe_fn_abs g]with x hx hxf hxg
rw [hxf, hxg] at hx
- exact solid hx }
+ exact HasSolidNorm.solid hx }
end Order
mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee
@@ -28,7 +28,7 @@ import Mathbin.MeasureTheory.Function.LpSpace
open TopologicalSpace MeasureTheory LatticeOrderedCommGroup
-open Ennreal
+open ENNReal
variable {α E : Type _} {m : MeasurableSpace α} {μ : Measure α} {p : ℝ≥0∞}
@@ -108,7 +108,7 @@ noncomputable instance [Fact (1 ≤ p)] : NormedLatticeAddCommGroup (lp E p μ)
add_le_add_left := fun f g => add_le_add_left
solid := fun f g hfg => by
rw [← coe_fn_le] at hfg
- simp_rw [Lp.norm_def, Ennreal.toReal_le_toReal (Lp.snorm_ne_top f) (Lp.snorm_ne_top g)]
+ simp_rw [Lp.norm_def, ENNReal.toReal_le_toReal (Lp.snorm_ne_top f) (Lp.snorm_ne_top g)]
refine' snorm_mono_ae _
filter_upwards [hfg, Lp.coe_fn_abs f, Lp.coe_fn_abs g]with x hx hxf hxg
rw [hxf, hxg] at hx
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -25,8 +25,7 @@ import Mathlib.MeasureTheory.Function.LpSpace
set_option linter.uppercaseLean3 false
-open TopologicalSpace MeasureTheory LatticeOrderedCommGroup
-
+open TopologicalSpace MeasureTheory
open scoped ENNReal
variable {α E : Type*} {m : MeasurableSpace α} {μ : Measure α} {p : ℝ≥0∞}
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -29,7 +29,7 @@ open TopologicalSpace MeasureTheory LatticeOrderedCommGroup
open scoped ENNReal
-variable {α E : Type _} {m : MeasurableSpace α} {μ : Measure α} {p : ℝ≥0∞}
+variable {α E : Type*} {m : MeasurableSpace α} {μ : Measure α} {p : ℝ≥0∞}
namespace MeasureTheory
@@ -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.lp_order
-! leanprover-community/mathlib commit 5dc275ec639221ca4d5f56938eb966f6ad9bc89f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Analysis.Normed.Order.Lattice
import Mathlib.MeasureTheory.Function.LpSpace
+#align_import measure_theory.function.lp_order from "leanprover-community/mathlib"@"5dc275ec639221ca4d5f56938eb966f6ad9bc89f"
+
/-!
# Order related properties of Lp spaces
@@ -79,7 +79,7 @@ theorem _root_.MeasureTheory.Memℒp.inf {f g : α → E} (hf : Memℒp f p μ)
(Filter.eventually_of_forall fun x => norm_inf_le_add (f x) (g x))
#align measure_theory.mem_ℒp.inf MeasureTheory.Memℒp.inf
-theorem _root_.MeasureTheory.Memℒp.abs {f : α → E} (hf : Memℒp f p μ) : Memℒp (|f|) p μ :=
+theorem _root_.MeasureTheory.Memℒp.abs {f : α → E} (hf : Memℒp f p μ) : Memℒp |f| p μ :=
hf.sup hf.neg
#align measure_theory.mem_ℒp.abs MeasureTheory.Memℒp.abs
@@ -101,7 +101,7 @@ theorem coeFn_inf (f g : Lp E p μ) : ⇑(f ⊓ g) =ᵐ[μ] ⇑f ⊓ ⇑g :=
AEEqFun.coeFn_inf _ _
#align measure_theory.Lp.coe_fn_inf MeasureTheory.Lp.coeFn_inf
-theorem coeFn_abs (f : Lp E p μ) : ⇑(|f|) =ᵐ[μ] fun x => |f x| :=
+theorem coeFn_abs (f : Lp E p μ) : ⇑|f| =ᵐ[μ] fun x => |f x| :=
AEEqFun.coeFn_abs _
#align measure_theory.Lp.coe_fn_abs MeasureTheory.Lp.coeFn_abs
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