measure_theory.category.Meas
⟷
Mathlib.MeasureTheory.Category.MeasCat
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
@@ -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"
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -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
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -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"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -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
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -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. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/c471da714c044131b90c133701e51b877c246677
@@ -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. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3
@@ -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
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: 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
+-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -36,7 +36,7 @@ noncomputable section
open CategoryTheory MeasureTheory
-open ENNReal
+open scoped ENNReal
universe u v
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -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]
mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952
@@ -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]
mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee
@@ -36,7 +36,7 @@ noncomputable section
open CategoryTheory MeasureTheory
-open Ennreal
+open ENNReal
universe u v
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -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 :=
@@ -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
@@ -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
@@ -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
The unported dependencies are
algebra.order.module
init.core
algebra.order.monoid.cancel.defs
algebra.abs
algebra.group_power.lemmas
init.data.list.basic
init.data.list.default
algebra.order.monoid.cancel.basic
topology.subset_properties
init.logic
The following 1 dependencies have changed in mathlib3 since they were ported, which may complicate porting this file