measure_theory.category.MeasMathlib.MeasureTheory.Category.MeasCat

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
@@ -6,7 +6,7 @@ Authors: Johannes Hölzl
 import MeasureTheory.Measure.GiryMonad
 import CategoryTheory.ConcreteCategory.UnbundledHom
 import CategoryTheory.Monad.Algebra
-import Topology.Category.Top.Basic
+import Topology.Category.TopCat.Basic
 
 #align_import measure_theory.category.Meas from "leanprover-community/mathlib"@"61b5e2755ccb464b68d05a9acf891ae04992d09d"
 
Diff
@@ -94,7 +94,7 @@ def Measure : MeasCat ⥤ MeasCat
     where
   obj X := ⟨@MeasureTheory.Measure X.1 X.2⟩
   map X Y f := ⟨Measure.map (f : X → Y), Measure.measurable_map f f.2⟩
-  map_id' := fun ⟨α, I⟩ => Subtype.eq <| funext fun μ => @Measure.map_id α I μ
+  map_id'' := fun ⟨α, I⟩ => Subtype.eq <| funext fun μ => @Measure.map_id α I μ
   map_comp' := fun X Y Z ⟨f, hf⟩ ⟨g, hg⟩ =>
     Subtype.eq <| funext fun μ => (Measure.map_map hg hf).symm
 #align Meas.Measure MeasCat.Measure
Diff
@@ -3,10 +3,10 @@ Copyright (c) 2018 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 -/
-import Mathbin.MeasureTheory.Measure.GiryMonad
-import Mathbin.CategoryTheory.ConcreteCategory.UnbundledHom
-import Mathbin.CategoryTheory.Monad.Algebra
-import Mathbin.Topology.Category.Top.Basic
+import MeasureTheory.Measure.GiryMonad
+import CategoryTheory.ConcreteCategory.UnbundledHom
+import CategoryTheory.Monad.Algebra
+import Topology.Category.Top.Basic
 
 #align_import measure_theory.category.Meas from "leanprover-community/mathlib"@"61b5e2755ccb464b68d05a9acf891ae04992d09d"
 
Diff
@@ -2,17 +2,14 @@
 Copyright (c) 2018 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
-
-! This file was ported from Lean 3 source module measure_theory.category.Meas
-! leanprover-community/mathlib commit 61b5e2755ccb464b68d05a9acf891ae04992d09d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Measure.GiryMonad
 import Mathbin.CategoryTheory.ConcreteCategory.UnbundledHom
 import Mathbin.CategoryTheory.Monad.Algebra
 import Mathbin.Topology.Category.Top.Basic
 
+#align_import measure_theory.category.Meas from "leanprover-community/mathlib"@"61b5e2755ccb464b68d05a9acf891ae04992d09d"
+
 /-!
 # The category of measurable spaces
 
Diff
@@ -139,9 +139,11 @@ def Integral : Giry.Algebra where
 
 end MeasCat
 
+#print TopCat.hasForgetToMeasCat /-
 instance TopCat.hasForgetToMeasCat : HasForget₂ TopCat.{u} MeasCat.{u} :=
   BundledHom.mkHasForget₂ borel (fun X Y f => ⟨f.1, f.2.borel_measurable⟩) (by intros <;> rfl)
 #align Top.has_forget_to_Meas TopCat.hasForgetToMeasCat
+-/
 
 #print Borel /-
 /-- The Borel functor, the canonical embedding of topological spaces into measurable spaces. -/
Diff
@@ -139,11 +139,9 @@ def Integral : Giry.Algebra where
 
 end MeasCat
 
-#print TopCat.hasForgetToMeasCat /-
 instance TopCat.hasForgetToMeasCat : HasForget₂ TopCat.{u} MeasCat.{u} :=
   BundledHom.mkHasForget₂ borel (fun X Y f => ⟨f.1, f.2.borel_measurable⟩) (by intros <;> rfl)
 #align Top.has_forget_to_Meas TopCat.hasForgetToMeasCat
--/
 
 #print Borel /-
 /-- The Borel functor, the canonical embedding of topological spaces into measurable spaces. -/
Diff
@@ -131,7 +131,7 @@ def Integral : Giry.Algebra where
   assoc' :=
     Subtype.eq <|
       funext fun μ : Measure (Measure ℝ≥0∞) =>
-        show (∫⁻ x, x ∂μ.join) = ∫⁻ x, x ∂Measure.map (fun m : Measure ℝ≥0∞ => ∫⁻ x, x ∂m) μ by
+        show ∫⁻ x, x ∂μ.join = ∫⁻ x, x ∂Measure.map (fun m : Measure ℝ≥0∞ => ∫⁻ x, x ∂m) μ by
           rw [measure.lintegral_join, lintegral_map] <;>
             apply_rules [measurable_id, measure.measurable_lintegral]
 #align Meas.Integral MeasCat.Integral
Diff
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 
 ! This file was ported from Lean 3 source module measure_theory.category.Meas
-! leanprover-community/mathlib commit d6814c584384ddf2825ff038e868451a7c956f31
+! leanprover-community/mathlib commit 61b5e2755ccb464b68d05a9acf891ae04992d09d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Topology.Category.Top.Basic
 /-!
 # The category of measurable spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Measurable spaces and measurable functions form a (concrete) category `Meas`.
 
 ## Main definitions
@@ -40,38 +43,47 @@ open scoped ENNReal
 
 universe u v
 
+#print MeasCat /-
 /-- The category of measurable spaces and measurable functions. -/
-def Meas : Type (u + 1) :=
+def MeasCat : Type (u + 1) :=
   Bundled MeasurableSpace
-#align Meas Meas
+#align Meas MeasCat
+-/
 
-namespace Meas
+namespace MeasCat
 
-instance : CoeSort Meas (Type _) :=
+instance : CoeSort MeasCat (Type _) :=
   Bundled.hasCoeToSort
 
-instance (X : Meas) : MeasurableSpace X :=
+instance (X : MeasCat) : MeasurableSpace X :=
   X.str
 
+#print MeasCat.of /-
 /-- Construct a bundled `Meas` from the underlying type and the typeclass. -/
-def of (α : Type u) [MeasurableSpace α] : Meas :=
+def of (α : Type u) [MeasurableSpace α] : MeasCat :=
   ⟨α⟩
-#align Meas.of Meas.of
+#align Meas.of MeasCat.of
+-/
 
+#print MeasCat.coe_of /-
 @[simp]
 theorem coe_of (X : Type u) [MeasurableSpace X] : (of X : Type u) = X :=
   rfl
-#align Meas.coe_of Meas.coe_of
+#align Meas.coe_of MeasCat.coe_of
+-/
 
+#print MeasCat.unbundledHom /-
 instance unbundledHom : UnbundledHom @Measurable :=
   ⟨@measurable_id, @Measurable.comp⟩
-#align Meas.unbundled_hom Meas.unbundledHom
+#align Meas.unbundled_hom MeasCat.unbundledHom
+-/
 
-deriving instance LargeCategory, ConcreteCategory for Meas
+deriving instance LargeCategory, ConcreteCategory for MeasCat
 
-instance : Inhabited Meas :=
-  ⟨Meas.of Empty⟩
+instance : Inhabited MeasCat :=
+  ⟨MeasCat.of Empty⟩
 
+#print MeasCat.Measure /-
 /-- `Measure X` is the measurable space of measures over the measurable space `X`. It is the
 weakest measurable space, s.t. λμ, μ s is measurable for all measurable sets `s` in `X`. An
 important purpose is to assign a monadic structure on it, the Giry monad. In the Giry monad,
@@ -81,18 +93,21 @@ the pure values are the Dirac measure, and the bind operation maps to the integr
 In probability theory, the `Meas`-morphisms `X → Prob X` are (sub-)Markov kernels (here `Prob` is
 the restriction of `Measure` to (sub-)probability space.)
 -/
-def measure : Meas ⥤ Meas where
+def Measure : MeasCat ⥤ MeasCat
+    where
   obj X := ⟨@MeasureTheory.Measure X.1 X.2⟩
   map X Y f := ⟨Measure.map (f : X → Y), Measure.measurable_map f f.2⟩
   map_id' := fun ⟨α, I⟩ => Subtype.eq <| funext fun μ => @Measure.map_id α I μ
   map_comp' := fun X Y Z ⟨f, hf⟩ ⟨g, hg⟩ =>
     Subtype.eq <| funext fun μ => (Measure.map_map hg hf).symm
-#align Meas.Measure Meas.measure
+#align Meas.Measure MeasCat.Measure
+-/
 
+#print MeasCat.Giry /-
 /-- The Giry monad, i.e. the monadic structure associated with `Measure`. -/
-def giry : CategoryTheory.Monad Meas
+def Giry : CategoryTheory.Monad MeasCat
     where
-  toFunctor := measure
+  toFunctor := Measure
   η' :=
     { app := fun X => ⟨@Measure.dirac X.1 X.2, Measure.measurable_dirac⟩
       naturality' := fun X Y ⟨f, hf⟩ =>
@@ -103,12 +118,14 @@ def giry : CategoryTheory.Monad Meas
   assoc' α := Subtype.eq <| funext fun μ => @Measure.join_map_join _ _ _
   left_unit' α := Subtype.eq <| funext fun μ => @Measure.join_dirac _ _ _
   right_unit' α := Subtype.eq <| funext fun μ => @Measure.join_map_dirac _ _ _
-#align Meas.Giry Meas.giry
+#align Meas.Giry MeasCat.Giry
+-/
 
+#print MeasCat.Integral /-
 /-- An example for an algebra on `Measure`: the nonnegative Lebesgue integral is a hom, behaving
 nicely under the monad operations. -/
-def integral : giry.Algebra where
-  A := Meas.of ℝ≥0∞
+def Integral : Giry.Algebra where
+  A := MeasCat.of ℝ≥0∞
   a := ⟨fun m : Measure ℝ≥0∞ => ∫⁻ x, x ∂m, Measure.measurable_lintegral measurable_id⟩
   unit' := Subtype.eq <| funext fun r : ℝ≥0∞ => lintegral_dirac' _ measurable_id
   assoc' :=
@@ -117,19 +134,22 @@ def integral : giry.Algebra where
         show (∫⁻ x, x ∂μ.join) = ∫⁻ x, x ∂Measure.map (fun m : Measure ℝ≥0∞ => ∫⁻ x, x ∂m) μ by
           rw [measure.lintegral_join, lintegral_map] <;>
             apply_rules [measurable_id, measure.measurable_lintegral]
-#align Meas.Integral Meas.integral
+#align Meas.Integral MeasCat.Integral
+-/
 
-end Meas
+end MeasCat
 
-instance TopCat.hasForgetToMeas : HasForget₂ TopCat.{u} Meas.{u} :=
+#print TopCat.hasForgetToMeasCat /-
+instance TopCat.hasForgetToMeasCat : HasForget₂ TopCat.{u} MeasCat.{u} :=
   BundledHom.mkHasForget₂ borel (fun X Y f => ⟨f.1, f.2.borel_measurable⟩) (by intros <;> rfl)
-#align Top.has_forget_to_Meas TopCat.hasForgetToMeas
+#align Top.has_forget_to_Meas TopCat.hasForgetToMeasCat
+-/
 
-/- warning: Borel clashes with borel -> borel
-Case conversion may be inaccurate. Consider using '#align Borel borelₓ'. -/
+#print Borel /-
 /-- The Borel functor, the canonical embedding of topological spaces into measurable spaces. -/
 @[reducible]
-def borel : TopCat.{u} ⥤ Meas.{u} :=
-  forget₂ TopCat.{u} Meas.{u}
-#align Borel borel
+def Borel : TopCat.{u} ⥤ MeasCat.{u} :=
+  forget₂ TopCat.{u} MeasCat.{u}
+#align Borel Borel
+-/
 
Diff
@@ -36,7 +36,7 @@ noncomputable section
 
 open CategoryTheory MeasureTheory
 
-open ENNReal
+open scoped ENNReal
 
 universe u v
 
Diff
@@ -126,11 +126,6 @@ instance TopCat.hasForgetToMeas : HasForget₂ TopCat.{u} Meas.{u} :=
 #align Top.has_forget_to_Meas TopCat.hasForgetToMeas
 
 /- warning: Borel clashes with borel -> borel
-warning: Borel -> borel is a dubious translation:
-lean 3 declaration is
-  CategoryTheory.Functor.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} Meas.{u1} Meas.largeCategory.{u1}
-but is expected to have type
-  forall (α : Type.{u1}) [inst._@.Mathlib.MeasureTheory.Constructions.BorelSpace.Basic._hyg.44 : TopologicalSpace.{u1} α], MeasurableSpace.{u1} α
 Case conversion may be inaccurate. Consider using '#align Borel borelₓ'. -/
 /-- The Borel functor, the canonical embedding of topological spaces into measurable spaces. -/
 @[reducible]
Diff
@@ -130,7 +130,7 @@ warning: Borel -> borel is a dubious translation:
 lean 3 declaration is
   CategoryTheory.Functor.{u1, u1, succ u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} Meas.{u1} Meas.largeCategory.{u1}
 but is expected to have type
-  forall (α : Type.{u1}) [_inst_1 : TopologicalSpace.{u1} α], MeasurableSpace.{u1} α
+  forall (α : Type.{u1}) [inst._@.Mathlib.MeasureTheory.Constructions.BorelSpace.Basic._hyg.44 : TopologicalSpace.{u1} α], MeasurableSpace.{u1} α
 Case conversion may be inaccurate. Consider using '#align Borel borelₓ'. -/
 /-- The Borel functor, the canonical embedding of topological spaces into measurable spaces. -/
 @[reducible]
Diff
@@ -36,7 +36,7 @@ noncomputable section
 
 open CategoryTheory MeasureTheory
 
-open Ennreal
+open ENNReal
 
 universe u v
 

Changes in mathlib4

mathlib3
mathlib4
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
@@ -46,7 +46,7 @@ def MeasCat : Type (u + 1) :=
 
 namespace MeasCat
 
-instance : CoeSort MeasCat (Type _) :=
+instance : CoeSort MeasCat (Type*) :=
   Bundled.coeSort
 
 instance (X : MeasCat) : MeasurableSpace X :=
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
@@ -2,17 +2,14 @@
 Copyright (c) 2018 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
-
-! This file was ported from Lean 3 source module measure_theory.category.Meas
-! leanprover-community/mathlib commit d6814c584384ddf2825ff038e868451a7c956f31
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.MeasureTheory.Measure.GiryMonad
 import Mathlib.CategoryTheory.ConcreteCategory.UnbundledHom
 import Mathlib.CategoryTheory.Monad.Algebra
 import Mathlib.Topology.Category.TopCat.Basic
 
+#align_import measure_theory.category.Meas from "leanprover-community/mathlib"@"d6814c584384ddf2825ff038e868451a7c956f31"
+
 /-!
 # The category of measurable spaces
 
chore: remove superfluous parentheses around integrals (#5591)
Diff
@@ -117,7 +117,7 @@ def Integral : Giry.Algebra where
   a := ⟨fun m : MeasureTheory.Measure ℝ≥0∞ ↦ ∫⁻ x, x ∂m, Measure.measurable_lintegral measurable_id⟩
   unit := Subtype.eq <| funext fun r : ℝ≥0∞ => lintegral_dirac' _ measurable_id
   assoc := Subtype.eq <| funext fun μ : MeasureTheory.Measure (MeasureTheory.Measure ℝ≥0∞) =>
-    show (∫⁻ x, x ∂μ.join) = ∫⁻ x, x ∂Measure.map (fun m => ∫⁻ x, x ∂m) μ by
+    show ∫⁻ x, x ∂μ.join = ∫⁻ x, x ∂Measure.map (fun m => ∫⁻ x, x ∂m) μ by
       rw [Measure.lintegral_join, lintegral_map] <;>
         apply_rules [measurable_id, Measure.measurable_lintegral]
 #align Meas.Integral MeasCat.Integral
feat: port Order.Category.HeytAlgCat (#5021)

Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

Diff
@@ -72,6 +72,7 @@ instance unbundledHom : UnbundledHom @Measurable :=
 deriving instance LargeCategory for MeasCat
 
 -- Porting note: `deriving instance ConcreteCategory for MeasCat` didn't work. Define it manually.
+-- see https://github.com/leanprover-community/mathlib4/issues/5020
 instance : ConcreteCategory MeasCat := by
   unfold MeasCat
   infer_instance
feat: port MeasureTheory.Category.Meas (#4487)

Dependencies 10 + 709

710 files ported (98.6%)
308973 lines ported (98.3%)
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The unported dependencies are

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