measure_theory.function.strongly_measurable.inner
β·
Mathlib.MeasureTheory.Function.StronglyMeasurable.Inner
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
@@ -27,7 +27,7 @@ namespace MeasureTheory
namespace StronglyMeasurable
#print MeasureTheory.StronglyMeasurable.inner /-
-protected theorem inner {π : Type _} {E : Type _} [IsROrC π] [NormedAddCommGroup E]
+protected theorem inner {π : Type _} {E : Type _} [RCLike π] [NormedAddCommGroup E]
[InnerProductSpace π E] {m : MeasurableSpace Ξ±} {f g : Ξ± β E} (hf : StronglyMeasurable f)
(hg : StronglyMeasurable g) : StronglyMeasurable fun t => @inner π _ _ (f t) (g t) :=
Continuous.comp_stronglyMeasurable continuous_inner (hf.prod_mk hg)
@@ -38,22 +38,22 @@ end StronglyMeasurable
namespace AeStronglyMeasurable
-variable {m : MeasurableSpace Ξ±} {ΞΌ : Measure Ξ±} {π : Type _} {E : Type _} [IsROrC π]
+variable {m : MeasurableSpace Ξ±} {ΞΌ : Measure Ξ±} {π : Type _} {E : Type _} [RCLike π]
[NormedAddCommGroup E] [InnerProductSpace π E]
local notation "βͺ" x ", " y "β«" => @inner π _ _ x y
#print MeasureTheory.AEStronglyMeasurable.re /-
protected theorem re {f : Ξ± β π} (hf : AEStronglyMeasurable f ΞΌ) :
- AEStronglyMeasurable (fun x => IsROrC.re (f x)) ΞΌ :=
- IsROrC.continuous_re.comp_aestronglyMeasurable hf
+ AEStronglyMeasurable (fun x => RCLike.re (f x)) ΞΌ :=
+ RCLike.continuous_re.comp_aestronglyMeasurable hf
#align measure_theory.ae_strongly_measurable.re MeasureTheory.AEStronglyMeasurable.re
-/
#print MeasureTheory.AEStronglyMeasurable.im /-
protected theorem im {f : Ξ± β π} (hf : AEStronglyMeasurable f ΞΌ) :
- AEStronglyMeasurable (fun x => IsROrC.im (f x)) ΞΌ :=
- IsROrC.continuous_im.comp_aestronglyMeasurable hf
+ AEStronglyMeasurable (fun x => RCLike.im (f x)) ΞΌ :=
+ RCLike.continuous_im.comp_aestronglyMeasurable hf
#align measure_theory.ae_strongly_measurable.im MeasureTheory.AEStronglyMeasurable.im
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2021 RΓ©my Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: RΓ©my Degenne, SΓ©bastien GouΓ«zel
-/
-import Mathbin.MeasureTheory.Function.StronglyMeasurable.Basic
-import Mathbin.Analysis.InnerProductSpace.Basic
+import MeasureTheory.Function.StronglyMeasurable.Basic
+import Analysis.InnerProductSpace.Basic
#align_import measure_theory.function.strongly_measurable.inner from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2021 RΓ©my Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: RΓ©my Degenne, SΓ©bastien GouΓ«zel
-
-! This file was ported from Lean 3 source module measure_theory.function.strongly_measurable.inner
-! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.MeasureTheory.Function.StronglyMeasurable.Basic
import Mathbin.Analysis.InnerProductSpace.Basic
+#align_import measure_theory.function.strongly_measurable.inner from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
+
/-!
# Inner products of strongly measurable functions are strongly measurable.
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -29,11 +29,13 @@ namespace MeasureTheory
namespace StronglyMeasurable
+#print MeasureTheory.StronglyMeasurable.inner /-
protected theorem inner {π : Type _} {E : Type _} [IsROrC π] [NormedAddCommGroup E]
[InnerProductSpace π E] {m : MeasurableSpace Ξ±} {f g : Ξ± β E} (hf : StronglyMeasurable f)
(hg : StronglyMeasurable g) : StronglyMeasurable fun t => @inner π _ _ (f t) (g t) :=
Continuous.comp_stronglyMeasurable continuous_inner (hf.prod_mk hg)
#align measure_theory.strongly_measurable.inner MeasureTheory.StronglyMeasurable.inner
+-/
end StronglyMeasurable
@@ -42,24 +44,29 @@ namespace AeStronglyMeasurable
variable {m : MeasurableSpace Ξ±} {ΞΌ : Measure Ξ±} {π : Type _} {E : Type _} [IsROrC π]
[NormedAddCommGroup E] [InnerProductSpace π E]
--- mathport name: Β«exprβͺ , β«Β»
local notation "βͺ" x ", " y "β«" => @inner π _ _ x y
+#print MeasureTheory.AEStronglyMeasurable.re /-
protected theorem re {f : Ξ± β π} (hf : AEStronglyMeasurable f ΞΌ) :
AEStronglyMeasurable (fun x => IsROrC.re (f x)) ΞΌ :=
IsROrC.continuous_re.comp_aestronglyMeasurable hf
#align measure_theory.ae_strongly_measurable.re MeasureTheory.AEStronglyMeasurable.re
+-/
+#print MeasureTheory.AEStronglyMeasurable.im /-
protected theorem im {f : Ξ± β π} (hf : AEStronglyMeasurable f ΞΌ) :
AEStronglyMeasurable (fun x => IsROrC.im (f x)) ΞΌ :=
IsROrC.continuous_im.comp_aestronglyMeasurable hf
#align measure_theory.ae_strongly_measurable.im MeasureTheory.AEStronglyMeasurable.im
+-/
+#print MeasureTheory.AEStronglyMeasurable.inner /-
protected theorem inner {m : MeasurableSpace Ξ±} {ΞΌ : Measure Ξ±} {f g : Ξ± β E}
(hf : AEStronglyMeasurable f ΞΌ) (hg : AEStronglyMeasurable g ΞΌ) :
AEStronglyMeasurable (fun x => βͺf x, g xβ«) ΞΌ :=
continuous_inner.comp_aestronglyMeasurable (hf.prod_mk hg)
#align measure_theory.ae_strongly_measurable.inner MeasureTheory.AEStronglyMeasurable.inner
+-/
end AeStronglyMeasurable
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -29,12 +29,6 @@ namespace MeasureTheory
namespace StronglyMeasurable
-/- warning: measure_theory.strongly_measurable.inner -> MeasureTheory.StronglyMeasurable.inner is a dubious translation:
-lean 3 declaration is
- forall {Ξ± : Type.{u1}} {π : Type.{u2}} {E : Type.{u3}} [_inst_1 : IsROrC.{u2} π] [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : InnerProductSpace.{u2, u3} π E _inst_1 _inst_2] {m : MeasurableSpace.{u1} Ξ±} {f : Ξ± -> E} {g : Ξ± -> E}, (MeasureTheory.StronglyMeasurable.{u1, u3} Ξ± E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) m f) -> (MeasureTheory.StronglyMeasurable.{u1, u3} Ξ± E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) m g) -> (MeasureTheory.StronglyMeasurable.{u1, u2} Ξ± π (UniformSpace.toTopologicalSpace.{u2} π (PseudoMetricSpace.toUniformSpace.{u2} π (SeminormedRing.toPseudoMetricSpace.{u2} π (SeminormedCommRing.toSemiNormedRing.{u2} π (NormedCommRing.toSeminormedCommRing.{u2} π (NormedField.toNormedCommRing.{u2} π (DenselyNormedField.toNormedField.{u2} π (IsROrC.toDenselyNormedField.{u2} π _inst_1)))))))) m (fun (t : Ξ±) => Inner.inner.{u2, u3} π E (InnerProductSpace.toHasInner.{u2, u3} π E _inst_1 _inst_2 _inst_3) (f t) (g t)))
-but is expected to have type
- forall {Ξ± : Type.{u1}} {π : Type.{u3}} {E : Type.{u2}} [_inst_1 : IsROrC.{u3} π] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : InnerProductSpace.{u3, u2} π E _inst_1 _inst_2] {m : MeasurableSpace.{u1} Ξ±} {f : Ξ± -> E} {g : Ξ± -> E}, (MeasureTheory.StronglyMeasurable.{u1, u2} Ξ± E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) m f) -> (MeasureTheory.StronglyMeasurable.{u1, u2} Ξ± E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) m g) -> (MeasureTheory.StronglyMeasurable.{u1, u3} Ξ± π (UniformSpace.toTopologicalSpace.{u3} π (PseudoMetricSpace.toUniformSpace.{u3} π (SeminormedRing.toPseudoMetricSpace.{u3} π (SeminormedCommRing.toSeminormedRing.{u3} π (NormedCommRing.toSeminormedCommRing.{u3} π (NormedField.toNormedCommRing.{u3} π (DenselyNormedField.toNormedField.{u3} π (IsROrC.toDenselyNormedField.{u3} π _inst_1)))))))) m (fun (t : Ξ±) => Inner.inner.{u3, u2} π E (InnerProductSpace.toInner.{u3, u2} π E _inst_1 _inst_2 _inst_3) (f t) (g t)))
-Case conversion may be inaccurate. Consider using '#align measure_theory.strongly_measurable.inner MeasureTheory.StronglyMeasurable.innerβ'. -/
protected theorem inner {π : Type _} {E : Type _} [IsROrC π] [NormedAddCommGroup E]
[InnerProductSpace π E] {m : MeasurableSpace Ξ±} {f g : Ξ± β E} (hf : StronglyMeasurable f)
(hg : StronglyMeasurable g) : StronglyMeasurable fun t => @inner π _ _ (f t) (g t) :=
@@ -51,28 +45,16 @@ variable {m : MeasurableSpace Ξ±} {ΞΌ : Measure Ξ±} {π : Type _} {E : Type _}
-- mathport name: Β«exprβͺ , β«Β»
local notation "βͺ" x ", " y "β«" => @inner π _ _ x y
-/- warning: measure_theory.ae_strongly_measurable.re -> MeasureTheory.AEStronglyMeasurable.re is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align measure_theory.ae_strongly_measurable.re MeasureTheory.AEStronglyMeasurable.reβ'. -/
protected theorem re {f : Ξ± β π} (hf : AEStronglyMeasurable f ΞΌ) :
AEStronglyMeasurable (fun x => IsROrC.re (f x)) ΞΌ :=
IsROrC.continuous_re.comp_aestronglyMeasurable hf
#align measure_theory.ae_strongly_measurable.re MeasureTheory.AEStronglyMeasurable.re
-/- warning: measure_theory.ae_strongly_measurable.im -> MeasureTheory.AEStronglyMeasurable.im is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align measure_theory.ae_strongly_measurable.im MeasureTheory.AEStronglyMeasurable.imβ'. -/
protected theorem im {f : Ξ± β π} (hf : AEStronglyMeasurable f ΞΌ) :
AEStronglyMeasurable (fun x => IsROrC.im (f x)) ΞΌ :=
IsROrC.continuous_im.comp_aestronglyMeasurable hf
#align measure_theory.ae_strongly_measurable.im MeasureTheory.AEStronglyMeasurable.im
-/- warning: measure_theory.ae_strongly_measurable.inner -> MeasureTheory.AEStronglyMeasurable.inner is a dubious translation:
-lean 3 declaration is
- forall {Ξ± : Type.{u1}} {π : Type.{u2}} {E : Type.{u3}} [_inst_1 : IsROrC.{u2} π] [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : InnerProductSpace.{u2, u3} π E _inst_1 _inst_2] {m : MeasurableSpace.{u1} Ξ±} {ΞΌ : MeasureTheory.Measure.{u1} Ξ± m} {f : Ξ± -> E} {g : Ξ± -> E}, (MeasureTheory.AEStronglyMeasurable.{u1, u3} Ξ± E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) m f ΞΌ) -> (MeasureTheory.AEStronglyMeasurable.{u1, u3} Ξ± E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) m g ΞΌ) -> (MeasureTheory.AEStronglyMeasurable.{u1, u2} Ξ± π (UniformSpace.toTopologicalSpace.{u2} π (PseudoMetricSpace.toUniformSpace.{u2} π (SeminormedRing.toPseudoMetricSpace.{u2} π (SeminormedCommRing.toSemiNormedRing.{u2} π (NormedCommRing.toSeminormedCommRing.{u2} π (NormedField.toNormedCommRing.{u2} π (DenselyNormedField.toNormedField.{u2} π (IsROrC.toDenselyNormedField.{u2} π _inst_1)))))))) m (fun (x : Ξ±) => Inner.inner.{u2, u3} π E (InnerProductSpace.toHasInner.{u2, u3} π E _inst_1 _inst_2 _inst_3) (f x) (g x)) ΞΌ)
-but is expected to have type
- forall {Ξ± : Type.{u3}} {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : IsROrC.{u1} π] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : InnerProductSpace.{u1, u2} π E _inst_1 _inst_2] {m : MeasurableSpace.{u3} Ξ±} {ΞΌ : MeasureTheory.Measure.{u3} Ξ± m} {f : Ξ± -> E} {g : Ξ± -> E}, (MeasureTheory.AEStronglyMeasurable.{u3, u2} Ξ± E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) m f ΞΌ) -> (MeasureTheory.AEStronglyMeasurable.{u3, u2} Ξ± E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) m g ΞΌ) -> (MeasureTheory.AEStronglyMeasurable.{u3, u1} Ξ± π (UniformSpace.toTopologicalSpace.{u1} π (PseudoMetricSpace.toUniformSpace.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1)))))))) m (fun (x : Ξ±) => Inner.inner.{u1, u2} π E (InnerProductSpace.toInner.{u1, u2} π E _inst_1 _inst_2 _inst_3) (f x) (g x)) ΞΌ)
-Case conversion may be inaccurate. Consider using '#align measure_theory.ae_strongly_measurable.inner MeasureTheory.AEStronglyMeasurable.innerβ'. -/
protected theorem inner {m : MeasurableSpace Ξ±} {ΞΌ : Measure Ξ±} {f g : Ξ± β E}
(hf : AEStronglyMeasurable f ΞΌ) (hg : AEStronglyMeasurable g ΞΌ) :
AEStronglyMeasurable (fun x => βͺf x, g xβ«) ΞΌ :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: RΓ©my Degenne, SΓ©bastien GouΓ«zel
! This file was ported from Lean 3 source module measure_theory.function.strongly_measurable.inner
-! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
+! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.Analysis.InnerProductSpace.Basic
/-!
# Inner products of strongly measurable functions are strongly measurable.
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
-/
@@ -49,10 +52,7 @@ variable {m : MeasurableSpace Ξ±} {ΞΌ : Measure Ξ±} {π : Type _} {E : Type _}
local notation "βͺ" x ", " y "β«" => @inner π _ _ x y
/- warning: measure_theory.ae_strongly_measurable.re -> MeasureTheory.AEStronglyMeasurable.re is a dubious translation:
-lean 3 declaration is
- forall {Ξ± : Type.{u1}} {m : MeasurableSpace.{u1} Ξ±} {ΞΌ : MeasureTheory.Measure.{u1} Ξ± m} {π : Type.{u2}} [_inst_1 : IsROrC.{u2} π] {f : Ξ± -> π}, (MeasureTheory.AEStronglyMeasurable.{u1, u2} Ξ± π (UniformSpace.toTopologicalSpace.{u2} π (PseudoMetricSpace.toUniformSpace.{u2} π (SeminormedRing.toPseudoMetricSpace.{u2} π (SeminormedCommRing.toSemiNormedRing.{u2} π (NormedCommRing.toSeminormedCommRing.{u2} π (NormedField.toNormedCommRing.{u2} π (DenselyNormedField.toNormedField.{u2} π (IsROrC.toDenselyNormedField.{u2} π _inst_1)))))))) m f ΞΌ) -> (MeasureTheory.AEStronglyMeasurable.{u1, 0} Ξ± Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) m (fun (x : Ξ±) => coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} π Real (AddMonoid.toAddZeroClass.{u2} π (AddMonoidWithOne.toAddMonoid.{u2} π (AddGroupWithOne.toAddMonoidWithOne.{u2} π (AddCommGroupWithOne.toAddGroupWithOne.{u2} π (Ring.toAddCommGroupWithOne.{u2} π (NormedRing.toRing.{u2} π (NormedCommRing.toNormedRing.{u2} π (NormedField.toNormedCommRing.{u2} π (DenselyNormedField.toNormedField.{u2} π (IsROrC.toDenselyNormedField.{u2} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} π Real (AddMonoid.toAddZeroClass.{u2} π (AddMonoidWithOne.toAddMonoid.{u2} π (AddGroupWithOne.toAddMonoidWithOne.{u2} π (AddCommGroupWithOne.toAddGroupWithOne.{u2} π (Ring.toAddCommGroupWithOne.{u2} π (NormedRing.toRing.{u2} π (NormedCommRing.toNormedRing.{u2} π (NormedField.toNormedCommRing.{u2} π (DenselyNormedField.toNormedField.{u2} π (IsROrC.toDenselyNormedField.{u2} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => π -> Real) (AddMonoidHom.hasCoeToFun.{u2, 0} π Real (AddMonoid.toAddZeroClass.{u2} π (AddMonoidWithOne.toAddMonoid.{u2} π (AddGroupWithOne.toAddMonoidWithOne.{u2} π (AddCommGroupWithOne.toAddGroupWithOne.{u2} π (Ring.toAddCommGroupWithOne.{u2} π (NormedRing.toRing.{u2} π (NormedCommRing.toNormedRing.{u2} π (NormedField.toNormedCommRing.{u2} π (DenselyNormedField.toNormedField.{u2} π (IsROrC.toDenselyNormedField.{u2} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u2} π _inst_1) (f x)) ΞΌ)
-but is expected to have type
- forall {Ξ± : Type.{u2}} {m : MeasurableSpace.{u2} Ξ±} {ΞΌ : MeasureTheory.Measure.{u2} Ξ± m} {π : Type.{u1}} [_inst_1 : IsROrC.{u1} π] {f : Ξ± -> π}, (MeasureTheory.AEStronglyMeasurable.{u2, u1} Ξ± π (UniformSpace.toTopologicalSpace.{u1} π (PseudoMetricSpace.toUniformSpace.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1)))))))) m f ΞΌ) -> (MeasureTheory.AEStronglyMeasurable.{u2, 0} Ξ± Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) m (fun (x : Ξ±) => FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) π (fun (_x : π) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : π) => Real) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) π Real (AddZeroClass.toAdd.{u1} π (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) π Real (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} π _inst_1) (f x)) ΞΌ)
+<too large>
Case conversion may be inaccurate. Consider using '#align measure_theory.ae_strongly_measurable.re MeasureTheory.AEStronglyMeasurable.reβ'. -/
protected theorem re {f : Ξ± β π} (hf : AEStronglyMeasurable f ΞΌ) :
AEStronglyMeasurable (fun x => IsROrC.re (f x)) ΞΌ :=
@@ -60,10 +60,7 @@ protected theorem re {f : Ξ± β π} (hf : AEStronglyMeasurable f ΞΌ) :
#align measure_theory.ae_strongly_measurable.re MeasureTheory.AEStronglyMeasurable.re
/- warning: measure_theory.ae_strongly_measurable.im -> MeasureTheory.AEStronglyMeasurable.im is a dubious translation:
-lean 3 declaration is
- forall {Ξ± : Type.{u1}} {m : MeasurableSpace.{u1} Ξ±} {ΞΌ : MeasureTheory.Measure.{u1} Ξ± m} {π : Type.{u2}} [_inst_1 : IsROrC.{u2} π] {f : Ξ± -> π}, (MeasureTheory.AEStronglyMeasurable.{u1, u2} Ξ± π (UniformSpace.toTopologicalSpace.{u2} π (PseudoMetricSpace.toUniformSpace.{u2} π (SeminormedRing.toPseudoMetricSpace.{u2} π (SeminormedCommRing.toSemiNormedRing.{u2} π (NormedCommRing.toSeminormedCommRing.{u2} π (NormedField.toNormedCommRing.{u2} π (DenselyNormedField.toNormedField.{u2} π (IsROrC.toDenselyNormedField.{u2} π _inst_1)))))))) m f ΞΌ) -> (MeasureTheory.AEStronglyMeasurable.{u1, 0} Ξ± Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) m (fun (x : Ξ±) => coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} π Real (AddMonoid.toAddZeroClass.{u2} π (AddMonoidWithOne.toAddMonoid.{u2} π (AddGroupWithOne.toAddMonoidWithOne.{u2} π (AddCommGroupWithOne.toAddGroupWithOne.{u2} π (Ring.toAddCommGroupWithOne.{u2} π (NormedRing.toRing.{u2} π (NormedCommRing.toNormedRing.{u2} π (NormedField.toNormedCommRing.{u2} π (DenselyNormedField.toNormedField.{u2} π (IsROrC.toDenselyNormedField.{u2} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} π Real (AddMonoid.toAddZeroClass.{u2} π (AddMonoidWithOne.toAddMonoid.{u2} π (AddGroupWithOne.toAddMonoidWithOne.{u2} π (AddCommGroupWithOne.toAddGroupWithOne.{u2} π (Ring.toAddCommGroupWithOne.{u2} π (NormedRing.toRing.{u2} π (NormedCommRing.toNormedRing.{u2} π (NormedField.toNormedCommRing.{u2} π (DenselyNormedField.toNormedField.{u2} π (IsROrC.toDenselyNormedField.{u2} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => π -> Real) (AddMonoidHom.hasCoeToFun.{u2, 0} π Real (AddMonoid.toAddZeroClass.{u2} π (AddMonoidWithOne.toAddMonoid.{u2} π (AddGroupWithOne.toAddMonoidWithOne.{u2} π (AddCommGroupWithOne.toAddGroupWithOne.{u2} π (Ring.toAddCommGroupWithOne.{u2} π (NormedRing.toRing.{u2} π (NormedCommRing.toNormedRing.{u2} π (NormedField.toNormedCommRing.{u2} π (DenselyNormedField.toNormedField.{u2} π (IsROrC.toDenselyNormedField.{u2} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u2} π _inst_1) (f x)) ΞΌ)
-but is expected to have type
- forall {Ξ± : Type.{u2}} {m : MeasurableSpace.{u2} Ξ±} {ΞΌ : MeasureTheory.Measure.{u2} Ξ± m} {π : Type.{u1}} [_inst_1 : IsROrC.{u1} π] {f : Ξ± -> π}, (MeasureTheory.AEStronglyMeasurable.{u2, u1} Ξ± π (UniformSpace.toTopologicalSpace.{u1} π (PseudoMetricSpace.toUniformSpace.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1)))))))) m f ΞΌ) -> (MeasureTheory.AEStronglyMeasurable.{u2, 0} Ξ± Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) m (fun (x : Ξ±) => FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) π (fun (_x : π) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : π) => Real) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) π Real (AddZeroClass.toAdd.{u1} π (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) π Real (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} π _inst_1) (f x)) ΞΌ)
+<too large>
Case conversion may be inaccurate. Consider using '#align measure_theory.ae_strongly_measurable.im MeasureTheory.AEStronglyMeasurable.imβ'. -/
protected theorem im {f : Ξ± β π} (hf : AEStronglyMeasurable f ΞΌ) :
AEStronglyMeasurable (fun x => IsROrC.im (f x)) ΞΌ :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/e1a18cad9cd462973d760af7de36b05776b8811c
@@ -26,6 +26,12 @@ namespace MeasureTheory
namespace StronglyMeasurable
+/- warning: measure_theory.strongly_measurable.inner -> MeasureTheory.StronglyMeasurable.inner is a dubious translation:
+lean 3 declaration is
+ forall {Ξ± : Type.{u1}} {π : Type.{u2}} {E : Type.{u3}} [_inst_1 : IsROrC.{u2} π] [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : InnerProductSpace.{u2, u3} π E _inst_1 _inst_2] {m : MeasurableSpace.{u1} Ξ±} {f : Ξ± -> E} {g : Ξ± -> E}, (MeasureTheory.StronglyMeasurable.{u1, u3} Ξ± E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) m f) -> (MeasureTheory.StronglyMeasurable.{u1, u3} Ξ± E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) m g) -> (MeasureTheory.StronglyMeasurable.{u1, u2} Ξ± π (UniformSpace.toTopologicalSpace.{u2} π (PseudoMetricSpace.toUniformSpace.{u2} π (SeminormedRing.toPseudoMetricSpace.{u2} π (SeminormedCommRing.toSemiNormedRing.{u2} π (NormedCommRing.toSeminormedCommRing.{u2} π (NormedField.toNormedCommRing.{u2} π (DenselyNormedField.toNormedField.{u2} π (IsROrC.toDenselyNormedField.{u2} π _inst_1)))))))) m (fun (t : Ξ±) => Inner.inner.{u2, u3} π E (InnerProductSpace.toHasInner.{u2, u3} π E _inst_1 _inst_2 _inst_3) (f t) (g t)))
+but is expected to have type
+ forall {Ξ± : Type.{u1}} {π : Type.{u3}} {E : Type.{u2}} [_inst_1 : IsROrC.{u3} π] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : InnerProductSpace.{u3, u2} π E _inst_1 _inst_2] {m : MeasurableSpace.{u1} Ξ±} {f : Ξ± -> E} {g : Ξ± -> E}, (MeasureTheory.StronglyMeasurable.{u1, u2} Ξ± E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) m f) -> (MeasureTheory.StronglyMeasurable.{u1, u2} Ξ± E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) m g) -> (MeasureTheory.StronglyMeasurable.{u1, u3} Ξ± π (UniformSpace.toTopologicalSpace.{u3} π (PseudoMetricSpace.toUniformSpace.{u3} π (SeminormedRing.toPseudoMetricSpace.{u3} π (SeminormedCommRing.toSeminormedRing.{u3} π (NormedCommRing.toSeminormedCommRing.{u3} π (NormedField.toNormedCommRing.{u3} π (DenselyNormedField.toNormedField.{u3} π (IsROrC.toDenselyNormedField.{u3} π _inst_1)))))))) m (fun (t : Ξ±) => Inner.inner.{u3, u2} π E (InnerProductSpace.toInner.{u3, u2} π E _inst_1 _inst_2 _inst_3) (f t) (g t)))
+Case conversion may be inaccurate. Consider using '#align measure_theory.strongly_measurable.inner MeasureTheory.StronglyMeasurable.innerβ'. -/
protected theorem inner {π : Type _} {E : Type _} [IsROrC π] [NormedAddCommGroup E]
[InnerProductSpace π E] {m : MeasurableSpace Ξ±} {f g : Ξ± β E} (hf : StronglyMeasurable f)
(hg : StronglyMeasurable g) : StronglyMeasurable fun t => @inner π _ _ (f t) (g t) :=
@@ -42,16 +48,34 @@ variable {m : MeasurableSpace Ξ±} {ΞΌ : Measure Ξ±} {π : Type _} {E : Type _}
-- mathport name: Β«exprβͺ , β«Β»
local notation "βͺ" x ", " y "β«" => @inner π _ _ x y
+/- warning: measure_theory.ae_strongly_measurable.re -> MeasureTheory.AEStronglyMeasurable.re is a dubious translation:
+lean 3 declaration is
+ forall {Ξ± : Type.{u1}} {m : MeasurableSpace.{u1} Ξ±} {ΞΌ : MeasureTheory.Measure.{u1} Ξ± m} {π : Type.{u2}} [_inst_1 : IsROrC.{u2} π] {f : Ξ± -> π}, (MeasureTheory.AEStronglyMeasurable.{u1, u2} Ξ± π (UniformSpace.toTopologicalSpace.{u2} π (PseudoMetricSpace.toUniformSpace.{u2} π (SeminormedRing.toPseudoMetricSpace.{u2} π (SeminormedCommRing.toSemiNormedRing.{u2} π (NormedCommRing.toSeminormedCommRing.{u2} π (NormedField.toNormedCommRing.{u2} π (DenselyNormedField.toNormedField.{u2} π (IsROrC.toDenselyNormedField.{u2} π _inst_1)))))))) m f ΞΌ) -> (MeasureTheory.AEStronglyMeasurable.{u1, 0} Ξ± Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) m (fun (x : Ξ±) => coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} π Real (AddMonoid.toAddZeroClass.{u2} π (AddMonoidWithOne.toAddMonoid.{u2} π (AddGroupWithOne.toAddMonoidWithOne.{u2} π (AddCommGroupWithOne.toAddGroupWithOne.{u2} π (Ring.toAddCommGroupWithOne.{u2} π (NormedRing.toRing.{u2} π (NormedCommRing.toNormedRing.{u2} π (NormedField.toNormedCommRing.{u2} π (DenselyNormedField.toNormedField.{u2} π (IsROrC.toDenselyNormedField.{u2} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} π Real (AddMonoid.toAddZeroClass.{u2} π (AddMonoidWithOne.toAddMonoid.{u2} π (AddGroupWithOne.toAddMonoidWithOne.{u2} π (AddCommGroupWithOne.toAddGroupWithOne.{u2} π (Ring.toAddCommGroupWithOne.{u2} π (NormedRing.toRing.{u2} π (NormedCommRing.toNormedRing.{u2} π (NormedField.toNormedCommRing.{u2} π (DenselyNormedField.toNormedField.{u2} π (IsROrC.toDenselyNormedField.{u2} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => π -> Real) (AddMonoidHom.hasCoeToFun.{u2, 0} π Real (AddMonoid.toAddZeroClass.{u2} π (AddMonoidWithOne.toAddMonoid.{u2} π (AddGroupWithOne.toAddMonoidWithOne.{u2} π (AddCommGroupWithOne.toAddGroupWithOne.{u2} π (Ring.toAddCommGroupWithOne.{u2} π (NormedRing.toRing.{u2} π (NormedCommRing.toNormedRing.{u2} π (NormedField.toNormedCommRing.{u2} π (DenselyNormedField.toNormedField.{u2} π (IsROrC.toDenselyNormedField.{u2} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u2} π _inst_1) (f x)) ΞΌ)
+but is expected to have type
+ forall {Ξ± : Type.{u2}} {m : MeasurableSpace.{u2} Ξ±} {ΞΌ : MeasureTheory.Measure.{u2} Ξ± m} {π : Type.{u1}} [_inst_1 : IsROrC.{u1} π] {f : Ξ± -> π}, (MeasureTheory.AEStronglyMeasurable.{u2, u1} Ξ± π (UniformSpace.toTopologicalSpace.{u1} π (PseudoMetricSpace.toUniformSpace.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1)))))))) m f ΞΌ) -> (MeasureTheory.AEStronglyMeasurable.{u2, 0} Ξ± Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) m (fun (x : Ξ±) => FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) π (fun (_x : π) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : π) => Real) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) π Real (AddZeroClass.toAdd.{u1} π (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) π Real (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} π _inst_1) (f x)) ΞΌ)
+Case conversion may be inaccurate. Consider using '#align measure_theory.ae_strongly_measurable.re MeasureTheory.AEStronglyMeasurable.reβ'. -/
protected theorem re {f : Ξ± β π} (hf : AEStronglyMeasurable f ΞΌ) :
AEStronglyMeasurable (fun x => IsROrC.re (f x)) ΞΌ :=
IsROrC.continuous_re.comp_aestronglyMeasurable hf
#align measure_theory.ae_strongly_measurable.re MeasureTheory.AEStronglyMeasurable.re
+/- warning: measure_theory.ae_strongly_measurable.im -> MeasureTheory.AEStronglyMeasurable.im is a dubious translation:
+lean 3 declaration is
+ forall {Ξ± : Type.{u1}} {m : MeasurableSpace.{u1} Ξ±} {ΞΌ : MeasureTheory.Measure.{u1} Ξ± m} {π : Type.{u2}} [_inst_1 : IsROrC.{u2} π] {f : Ξ± -> π}, (MeasureTheory.AEStronglyMeasurable.{u1, u2} Ξ± π (UniformSpace.toTopologicalSpace.{u2} π (PseudoMetricSpace.toUniformSpace.{u2} π (SeminormedRing.toPseudoMetricSpace.{u2} π (SeminormedCommRing.toSemiNormedRing.{u2} π (NormedCommRing.toSeminormedCommRing.{u2} π (NormedField.toNormedCommRing.{u2} π (DenselyNormedField.toNormedField.{u2} π (IsROrC.toDenselyNormedField.{u2} π _inst_1)))))))) m f ΞΌ) -> (MeasureTheory.AEStronglyMeasurable.{u1, 0} Ξ± Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) m (fun (x : Ξ±) => coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} π Real (AddMonoid.toAddZeroClass.{u2} π (AddMonoidWithOne.toAddMonoid.{u2} π (AddGroupWithOne.toAddMonoidWithOne.{u2} π (AddCommGroupWithOne.toAddGroupWithOne.{u2} π (Ring.toAddCommGroupWithOne.{u2} π (NormedRing.toRing.{u2} π (NormedCommRing.toNormedRing.{u2} π (NormedField.toNormedCommRing.{u2} π (DenselyNormedField.toNormedField.{u2} π (IsROrC.toDenselyNormedField.{u2} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} π Real (AddMonoid.toAddZeroClass.{u2} π (AddMonoidWithOne.toAddMonoid.{u2} π (AddGroupWithOne.toAddMonoidWithOne.{u2} π (AddCommGroupWithOne.toAddGroupWithOne.{u2} π (Ring.toAddCommGroupWithOne.{u2} π (NormedRing.toRing.{u2} π (NormedCommRing.toNormedRing.{u2} π (NormedField.toNormedCommRing.{u2} π (DenselyNormedField.toNormedField.{u2} π (IsROrC.toDenselyNormedField.{u2} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => π -> Real) (AddMonoidHom.hasCoeToFun.{u2, 0} π Real (AddMonoid.toAddZeroClass.{u2} π (AddMonoidWithOne.toAddMonoid.{u2} π (AddGroupWithOne.toAddMonoidWithOne.{u2} π (AddCommGroupWithOne.toAddGroupWithOne.{u2} π (Ring.toAddCommGroupWithOne.{u2} π (NormedRing.toRing.{u2} π (NormedCommRing.toNormedRing.{u2} π (NormedField.toNormedCommRing.{u2} π (DenselyNormedField.toNormedField.{u2} π (IsROrC.toDenselyNormedField.{u2} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u2} π _inst_1) (f x)) ΞΌ)
+but is expected to have type
+ forall {Ξ± : Type.{u2}} {m : MeasurableSpace.{u2} Ξ±} {ΞΌ : MeasureTheory.Measure.{u2} Ξ± m} {π : Type.{u1}} [_inst_1 : IsROrC.{u1} π] {f : Ξ± -> π}, (MeasureTheory.AEStronglyMeasurable.{u2, u1} Ξ± π (UniformSpace.toTopologicalSpace.{u1} π (PseudoMetricSpace.toUniformSpace.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1)))))))) m f ΞΌ) -> (MeasureTheory.AEStronglyMeasurable.{u2, 0} Ξ± Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) m (fun (x : Ξ±) => FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) π (fun (_x : π) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : π) => Real) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) π Real (AddZeroClass.toAdd.{u1} π (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) π Real (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (Semiring.toNonUnitalSemiring.{u1} π (Ring.toSemiring.{u1} π (CommRing.toRing.{u1} π (Field.toCommRing.{u1} π (NormedField.toField.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} π _inst_1) (f x)) ΞΌ)
+Case conversion may be inaccurate. Consider using '#align measure_theory.ae_strongly_measurable.im MeasureTheory.AEStronglyMeasurable.imβ'. -/
protected theorem im {f : Ξ± β π} (hf : AEStronglyMeasurable f ΞΌ) :
AEStronglyMeasurable (fun x => IsROrC.im (f x)) ΞΌ :=
IsROrC.continuous_im.comp_aestronglyMeasurable hf
#align measure_theory.ae_strongly_measurable.im MeasureTheory.AEStronglyMeasurable.im
+/- warning: measure_theory.ae_strongly_measurable.inner -> MeasureTheory.AEStronglyMeasurable.inner is a dubious translation:
+lean 3 declaration is
+ forall {Ξ± : Type.{u1}} {π : Type.{u2}} {E : Type.{u3}} [_inst_1 : IsROrC.{u2} π] [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : InnerProductSpace.{u2, u3} π E _inst_1 _inst_2] {m : MeasurableSpace.{u1} Ξ±} {ΞΌ : MeasureTheory.Measure.{u1} Ξ± m} {f : Ξ± -> E} {g : Ξ± -> E}, (MeasureTheory.AEStronglyMeasurable.{u1, u3} Ξ± E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) m f ΞΌ) -> (MeasureTheory.AEStronglyMeasurable.{u1, u3} Ξ± E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) m g ΞΌ) -> (MeasureTheory.AEStronglyMeasurable.{u1, u2} Ξ± π (UniformSpace.toTopologicalSpace.{u2} π (PseudoMetricSpace.toUniformSpace.{u2} π (SeminormedRing.toPseudoMetricSpace.{u2} π (SeminormedCommRing.toSemiNormedRing.{u2} π (NormedCommRing.toSeminormedCommRing.{u2} π (NormedField.toNormedCommRing.{u2} π (DenselyNormedField.toNormedField.{u2} π (IsROrC.toDenselyNormedField.{u2} π _inst_1)))))))) m (fun (x : Ξ±) => Inner.inner.{u2, u3} π E (InnerProductSpace.toHasInner.{u2, u3} π E _inst_1 _inst_2 _inst_3) (f x) (g x)) ΞΌ)
+but is expected to have type
+ forall {Ξ± : Type.{u3}} {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : IsROrC.{u1} π] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : InnerProductSpace.{u1, u2} π E _inst_1 _inst_2] {m : MeasurableSpace.{u3} Ξ±} {ΞΌ : MeasureTheory.Measure.{u3} Ξ± m} {f : Ξ± -> E} {g : Ξ± -> E}, (MeasureTheory.AEStronglyMeasurable.{u3, u2} Ξ± E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) m f ΞΌ) -> (MeasureTheory.AEStronglyMeasurable.{u3, u2} Ξ± E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) m g ΞΌ) -> (MeasureTheory.AEStronglyMeasurable.{u3, u1} Ξ± π (UniformSpace.toTopologicalSpace.{u1} π (PseudoMetricSpace.toUniformSpace.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1)))))))) m (fun (x : Ξ±) => Inner.inner.{u1, u2} π E (InnerProductSpace.toInner.{u1, u2} π E _inst_1 _inst_2 _inst_3) (f x) (g x)) ΞΌ)
+Case conversion may be inaccurate. Consider using '#align measure_theory.ae_strongly_measurable.inner MeasureTheory.AEStronglyMeasurable.innerβ'. -/
protected theorem inner {m : MeasurableSpace Ξ±} {ΞΌ : Measure Ξ±} {f g : Ξ± β E}
(hf : AEStronglyMeasurable f ΞΌ) (hg : AEStronglyMeasurable g ΞΌ) :
AEStronglyMeasurable (fun x => βͺf x, g xβ«) ΞΌ :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828
@@ -42,21 +42,21 @@ variable {m : MeasurableSpace Ξ±} {ΞΌ : Measure Ξ±} {π : Type _} {E : Type _}
-- mathport name: Β«exprβͺ , β«Β»
local notation "βͺ" x ", " y "β«" => @inner π _ _ x y
-protected theorem re {f : Ξ± β π} (hf : AeStronglyMeasurable f ΞΌ) :
- AeStronglyMeasurable (fun x => IsROrC.re (f x)) ΞΌ :=
- IsROrC.continuous_re.comp_aeStronglyMeasurable hf
-#align measure_theory.ae_strongly_measurable.re MeasureTheory.AeStronglyMeasurable.re
+protected theorem re {f : Ξ± β π} (hf : AEStronglyMeasurable f ΞΌ) :
+ AEStronglyMeasurable (fun x => IsROrC.re (f x)) ΞΌ :=
+ IsROrC.continuous_re.comp_aestronglyMeasurable hf
+#align measure_theory.ae_strongly_measurable.re MeasureTheory.AEStronglyMeasurable.re
-protected theorem im {f : Ξ± β π} (hf : AeStronglyMeasurable f ΞΌ) :
- AeStronglyMeasurable (fun x => IsROrC.im (f x)) ΞΌ :=
- IsROrC.continuous_im.comp_aeStronglyMeasurable hf
-#align measure_theory.ae_strongly_measurable.im MeasureTheory.AeStronglyMeasurable.im
+protected theorem im {f : Ξ± β π} (hf : AEStronglyMeasurable f ΞΌ) :
+ AEStronglyMeasurable (fun x => IsROrC.im (f x)) ΞΌ :=
+ IsROrC.continuous_im.comp_aestronglyMeasurable hf
+#align measure_theory.ae_strongly_measurable.im MeasureTheory.AEStronglyMeasurable.im
protected theorem inner {m : MeasurableSpace Ξ±} {ΞΌ : Measure Ξ±} {f g : Ξ± β E}
- (hf : AeStronglyMeasurable f ΞΌ) (hg : AeStronglyMeasurable g ΞΌ) :
- AeStronglyMeasurable (fun x => βͺf x, g xβ«) ΞΌ :=
- continuous_inner.comp_aeStronglyMeasurable (hf.prod_mk hg)
-#align measure_theory.ae_strongly_measurable.inner MeasureTheory.AeStronglyMeasurable.inner
+ (hf : AEStronglyMeasurable f ΞΌ) (hg : AEStronglyMeasurable g ΞΌ) :
+ AEStronglyMeasurable (fun x => βͺf x, g xβ«) ΞΌ :=
+ continuous_inner.comp_aestronglyMeasurable (hf.prod_mk hg)
+#align measure_theory.ae_strongly_measurable.inner MeasureTheory.AEStronglyMeasurable.inner
end AeStronglyMeasurable
mathlib commit https://github.com/leanprover-community/mathlib/commit/92c69b77c5a7dc0f7eeddb552508633305157caa
@@ -44,18 +44,18 @@ local notation "βͺ" x ", " y "β«" => @inner π _ _ x y
protected theorem re {f : Ξ± β π} (hf : AeStronglyMeasurable f ΞΌ) :
AeStronglyMeasurable (fun x => IsROrC.re (f x)) ΞΌ :=
- IsROrC.continuous_re.compAeStronglyMeasurable hf
+ IsROrC.continuous_re.comp_aeStronglyMeasurable hf
#align measure_theory.ae_strongly_measurable.re MeasureTheory.AeStronglyMeasurable.re
protected theorem im {f : Ξ± β π} (hf : AeStronglyMeasurable f ΞΌ) :
AeStronglyMeasurable (fun x => IsROrC.im (f x)) ΞΌ :=
- IsROrC.continuous_im.compAeStronglyMeasurable hf
+ IsROrC.continuous_im.comp_aeStronglyMeasurable hf
#align measure_theory.ae_strongly_measurable.im MeasureTheory.AeStronglyMeasurable.im
protected theorem inner {m : MeasurableSpace Ξ±} {ΞΌ : Measure Ξ±} {f g : Ξ± β E}
(hf : AeStronglyMeasurable f ΞΌ) (hg : AeStronglyMeasurable g ΞΌ) :
AeStronglyMeasurable (fun x => βͺf x, g xβ«) ΞΌ :=
- continuous_inner.compAeStronglyMeasurable (hf.prod_mk hg)
+ continuous_inner.comp_aeStronglyMeasurable (hf.prod_mk hg)
#align measure_theory.ae_strongly_measurable.inner MeasureTheory.AeStronglyMeasurable.inner
end AeStronglyMeasurable
mathlib commit https://github.com/leanprover-community/mathlib/commit/55d771df074d0dd020139ee1cd4b95521422df9f
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: RΓ©my Degenne, SΓ©bastien GouΓ«zel
! This file was ported from Lean 3 source module measure_theory.function.strongly_measurable.inner
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -26,9 +26,9 @@ namespace MeasureTheory
namespace StronglyMeasurable
-protected theorem inner {π : Type _} {E : Type _} [IsROrC π] [InnerProductSpace π E]
- {m : MeasurableSpace Ξ±} {f g : Ξ± β E} (hf : StronglyMeasurable f) (hg : StronglyMeasurable g) :
- StronglyMeasurable fun t => @inner π _ _ (f t) (g t) :=
+protected theorem inner {π : Type _} {E : Type _} [IsROrC π] [NormedAddCommGroup E]
+ [InnerProductSpace π E] {m : MeasurableSpace Ξ±} {f g : Ξ± β E} (hf : StronglyMeasurable f)
+ (hg : StronglyMeasurable g) : StronglyMeasurable fun t => @inner π _ _ (f t) (g t) :=
Continuous.comp_stronglyMeasurable continuous_inner (hf.prod_mk hg)
#align measure_theory.strongly_measurable.inner MeasureTheory.StronglyMeasurable.inner
@@ -37,7 +37,7 @@ end StronglyMeasurable
namespace AeStronglyMeasurable
variable {m : MeasurableSpace Ξ±} {ΞΌ : Measure Ξ±} {π : Type _} {E : Type _} [IsROrC π]
- [InnerProductSpace π E]
+ [NormedAddCommGroup E] [InnerProductSpace π E]
-- mathport name: Β«exprβͺ , β«Β»
local notation "βͺ" x ", " y "β«" => @inner π _ _ x y
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
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
.
@@ -23,7 +23,7 @@ namespace MeasureTheory
namespace StronglyMeasurable
-protected theorem inner {π : Type*} {E : Type*} [IsROrC π] [NormedAddCommGroup E]
+protected theorem inner {π : Type*} {E : Type*} [RCLike π] [NormedAddCommGroup E]
[InnerProductSpace π E] {_ : MeasurableSpace Ξ±} {f g : Ξ± β E} (hf : StronglyMeasurable f)
(hg : StronglyMeasurable g) : StronglyMeasurable fun t => @inner π _ _ (f t) (g t) :=
Continuous.comp_stronglyMeasurable continuous_inner (hf.prod_mk hg)
@@ -33,19 +33,19 @@ end StronglyMeasurable
namespace AEStronglyMeasurable
-variable {m : MeasurableSpace Ξ±} {ΞΌ : Measure Ξ±} {π : Type*} {E : Type*} [IsROrC π]
+variable {m : MeasurableSpace Ξ±} {ΞΌ : Measure Ξ±} {π : Type*} {E : Type*} [RCLike π]
[NormedAddCommGroup E] [InnerProductSpace π E]
local notation "βͺ" x ", " y "β«" => @inner π _ _ x y
protected theorem re {f : Ξ± β π} (hf : AEStronglyMeasurable f ΞΌ) :
- AEStronglyMeasurable (fun x => IsROrC.re (f x)) ΞΌ :=
- IsROrC.continuous_re.comp_aestronglyMeasurable hf
+ AEStronglyMeasurable (fun x => RCLike.re (f x)) ΞΌ :=
+ RCLike.continuous_re.comp_aestronglyMeasurable hf
#align measure_theory.ae_strongly_measurable.re MeasureTheory.AEStronglyMeasurable.re
protected theorem im {f : Ξ± β π} (hf : AEStronglyMeasurable f ΞΌ) :
- AEStronglyMeasurable (fun x => IsROrC.im (f x)) ΞΌ :=
- IsROrC.continuous_im.comp_aestronglyMeasurable hf
+ AEStronglyMeasurable (fun x => RCLike.im (f x)) ΞΌ :=
+ RCLike.continuous_im.comp_aestronglyMeasurable hf
#align measure_theory.ae_strongly_measurable.im MeasureTheory.AEStronglyMeasurable.im
protected theorem inner {_ : MeasurableSpace Ξ±} {ΞΌ : Measure Ξ±} {f g : Ξ± β E}
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -14,7 +14,7 @@ import Mathlib.Analysis.InnerProductSpace.Basic
-/
-variable {Ξ± : Type _}
+variable {Ξ± : Type*}
namespace MeasureTheory
@@ -23,7 +23,7 @@ namespace MeasureTheory
namespace StronglyMeasurable
-protected theorem inner {π : Type _} {E : Type _} [IsROrC π] [NormedAddCommGroup E]
+protected theorem inner {π : Type*} {E : Type*} [IsROrC π] [NormedAddCommGroup E]
[InnerProductSpace π E] {_ : MeasurableSpace Ξ±} {f g : Ξ± β E} (hf : StronglyMeasurable f)
(hg : StronglyMeasurable g) : StronglyMeasurable fun t => @inner π _ _ (f t) (g t) :=
Continuous.comp_stronglyMeasurable continuous_inner (hf.prod_mk hg)
@@ -33,7 +33,7 @@ end StronglyMeasurable
namespace AEStronglyMeasurable
-variable {m : MeasurableSpace Ξ±} {ΞΌ : Measure Ξ±} {π : Type _} {E : Type _} [IsROrC π]
+variable {m : MeasurableSpace Ξ±} {ΞΌ : Measure Ξ±} {π : Type*} {E : Type*} [IsROrC π]
[NormedAddCommGroup E] [InnerProductSpace π E]
local notation "βͺ" x ", " y "β«" => @inner π _ _ x y
@@ -2,15 +2,12 @@
Copyright (c) 2021 RΓ©my Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: RΓ©my Degenne, SΓ©bastien GouΓ«zel
-
-! This file was ported from Lean 3 source module measure_theory.function.strongly_measurable.inner
-! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic
import Mathlib.Analysis.InnerProductSpace.Basic
+#align_import measure_theory.function.strongly_measurable.inner from "leanprover-community/mathlib"@"46b633fd842bef9469441c0209906f6dddd2b4f5"
+
/-!
# Inner products of strongly measurable functions are strongly measurable.
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