measure_theory.function.lp_orderMathlib.MeasureTheory.Function.LpOrder

This file has been ported!

Changes since the initial port

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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Changes in mathlib3port

mathlib3
mathlib3port
Diff
@@ -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
Diff
@@ -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"
 
Diff
@@ -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
 
Diff
@@ -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
 -/
Diff
@@ -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,
Diff
@@ -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 }
 
Diff
@@ -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
Diff
@@ -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
Diff
@@ -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∞}
 
Diff
@@ -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) :=
Diff
@@ -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
 
Diff
@@ -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
 
Diff
@@ -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
 
Diff
@@ -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

Changes in mathlib4

mathlib3
mathlib4
refactor: Clean up posPart (#9740)

This changes the typeclass notation approach with plain functions.

Followup to #9553. Part of #9411

Diff
@@ -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∞}
chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

Diff
@@ -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
 
chore: script to replace headers with #align_import statements (#5979)

Open in Gitpod

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

Diff
@@ -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
 
fix: precedence of , and abs (#5619)
Diff
@@ -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
 
feat: port MeasureTheory.Function.LpOrder (#4374)

Co-authored-by: Jon Eugster <eugster.jon@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

Dependencies 12 + 931

932 files ported (98.7%)
422321 lines ported (98.7%)
Show graph

The unported dependencies are

The following 1 dependencies have changed in mathlib3 since they were ported, which may complicate porting this file