measure_theory.function.special_functions.is_R_or_C
β·
Mathlib.MeasureTheory.Function.SpecialFunctions.IsROrC
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
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import MeasureTheory.Function.SpecialFunctions.Basic
-import Data.IsROrC.Lemmas
+import Analysis.RCLike.Lemmas
#align_import measure_theory.function.special_functions.is_R_or_C from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
@@ -21,55 +21,55 @@ noncomputable section
open scoped NNReal ENNReal
-namespace IsROrC
+namespace RCLike
-variable {π : Type _} [IsROrC π]
+variable {π : Type _} [RCLike π]
-#print IsROrC.measurable_re /-
+#print RCLike.measurable_re /-
@[measurability]
theorem measurable_re : Measurable (re : π β β) :=
continuous_re.Measurable
-#align is_R_or_C.measurable_re IsROrC.measurable_re
+#align is_R_or_C.measurable_re RCLike.measurable_re
-/
-#print IsROrC.measurable_im /-
+#print RCLike.measurable_im /-
@[measurability]
theorem measurable_im : Measurable (im : π β β) :=
continuous_im.Measurable
-#align is_R_or_C.measurable_im IsROrC.measurable_im
+#align is_R_or_C.measurable_im RCLike.measurable_im
-/
-end IsROrC
+end RCLike
section IsROrCComposition
-variable {Ξ± π : Type _} [IsROrC π] {m : MeasurableSpace Ξ±} {f : Ξ± β π} {ΞΌ : MeasureTheory.Measure Ξ±}
+variable {Ξ± π : Type _} [RCLike π] {m : MeasurableSpace Ξ±} {f : Ξ± β π} {ΞΌ : MeasureTheory.Measure Ξ±}
#print Measurable.re /-
@[measurability]
-theorem Measurable.re (hf : Measurable f) : Measurable fun x => IsROrC.re (f x) :=
- IsROrC.measurable_re.comp hf
+theorem Measurable.re (hf : Measurable f) : Measurable fun x => RCLike.re (f x) :=
+ RCLike.measurable_re.comp hf
#align measurable.re Measurable.re
-/
#print AEMeasurable.re /-
@[measurability]
-theorem AEMeasurable.re (hf : AEMeasurable f ΞΌ) : AEMeasurable (fun x => IsROrC.re (f x)) ΞΌ :=
- IsROrC.measurable_re.comp_aemeasurable hf
+theorem AEMeasurable.re (hf : AEMeasurable f ΞΌ) : AEMeasurable (fun x => RCLike.re (f x)) ΞΌ :=
+ RCLike.measurable_re.comp_aemeasurable hf
#align ae_measurable.re AEMeasurable.re
-/
#print Measurable.im /-
@[measurability]
-theorem Measurable.im (hf : Measurable f) : Measurable fun x => IsROrC.im (f x) :=
- IsROrC.measurable_im.comp hf
+theorem Measurable.im (hf : Measurable f) : Measurable fun x => RCLike.im (f x) :=
+ RCLike.measurable_im.comp hf
#align measurable.im Measurable.im
-/
#print AEMeasurable.im /-
@[measurability]
-theorem AEMeasurable.im (hf : AEMeasurable f ΞΌ) : AEMeasurable (fun x => IsROrC.im (f x)) ΞΌ :=
- IsROrC.measurable_im.comp_aemeasurable hf
+theorem AEMeasurable.im (hf : AEMeasurable f ΞΌ) : AEMeasurable (fun x => RCLike.im (f x)) ΞΌ :=
+ RCLike.measurable_im.comp_aemeasurable hf
#align ae_measurable.im AEMeasurable.im
-/
@@ -77,37 +77,37 @@ end IsROrCComposition
section
-variable {Ξ± π : Type _} [IsROrC π] [MeasurableSpace Ξ±] {f : Ξ± β π} {ΞΌ : MeasureTheory.Measure Ξ±}
+variable {Ξ± π : Type _} [RCLike π] [MeasurableSpace Ξ±] {f : Ξ± β π} {ΞΌ : MeasureTheory.Measure Ξ±}
-#print IsROrC.measurable_ofReal /-
+#print RCLike.measurable_ofReal /-
@[measurability]
-theorem IsROrC.measurable_ofReal : Measurable (coe : β β π) :=
- IsROrC.continuous_ofReal.Measurable
-#align is_R_or_C.measurable_of_real IsROrC.measurable_ofReal
+theorem RCLike.measurable_ofReal : Measurable (coe : β β π) :=
+ RCLike.continuous_ofReal.Measurable
+#align is_R_or_C.measurable_of_real RCLike.measurable_ofReal
-/
#print measurable_of_re_im /-
-theorem measurable_of_re_im (hre : Measurable fun x => IsROrC.re (f x))
- (him : Measurable fun x => IsROrC.im (f x)) : Measurable f :=
+theorem measurable_of_re_im (hre : Measurable fun x => RCLike.re (f x))
+ (him : Measurable fun x => RCLike.im (f x)) : Measurable f :=
by
convert
(is_R_or_C.measurable_of_real.comp hre).add
- ((is_R_or_C.measurable_of_real.comp him).mul_const IsROrC.i)
+ ((is_R_or_C.measurable_of_real.comp him).mul_const RCLike.i)
Β· ext1 x
- exact (IsROrC.re_add_im _).symm
+ exact (RCLike.re_add_im _).symm
all_goals infer_instance
#align measurable_of_re_im measurable_of_re_im
-/
#print aemeasurable_of_re_im /-
-theorem aemeasurable_of_re_im (hre : AEMeasurable (fun x => IsROrC.re (f x)) ΞΌ)
- (him : AEMeasurable (fun x => IsROrC.im (f x)) ΞΌ) : AEMeasurable f ΞΌ :=
+theorem aemeasurable_of_re_im (hre : AEMeasurable (fun x => RCLike.re (f x)) ΞΌ)
+ (him : AEMeasurable (fun x => RCLike.im (f x)) ΞΌ) : AEMeasurable f ΞΌ :=
by
convert
(is_R_or_C.measurable_of_real.comp_ae_measurable hre).add
- ((is_R_or_C.measurable_of_real.comp_ae_measurable him).mul_const IsROrC.i)
+ ((is_R_or_C.measurable_of_real.comp_ae_measurable him).mul_const RCLike.i)
Β· ext1 x
- exact (IsROrC.re_add_im _).symm
+ exact (RCLike.re_add_im _).symm
all_goals infer_instance
#align ae_measurable_of_re_im aemeasurable_of_re_im
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
-import Mathbin.MeasureTheory.Function.SpecialFunctions.Basic
-import Mathbin.Data.IsROrC.Lemmas
+import MeasureTheory.Function.SpecialFunctions.Basic
+import Data.IsROrC.Lemmas
#align_import measure_theory.function.special_functions.is_R_or_C from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module measure_theory.function.special_functions.is_R_or_C
-! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.MeasureTheory.Function.SpecialFunctions.Basic
import Mathbin.Data.IsROrC.Lemmas
+#align_import measure_theory.function.special_functions.is_R_or_C from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
+
/-!
# Measurability of the basic `is_R_or_C` functions
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -28,15 +28,19 @@ namespace IsROrC
variable {π : Type _} [IsROrC π]
+#print IsROrC.measurable_re /-
@[measurability]
theorem measurable_re : Measurable (re : π β β) :=
continuous_re.Measurable
#align is_R_or_C.measurable_re IsROrC.measurable_re
+-/
+#print IsROrC.measurable_im /-
@[measurability]
theorem measurable_im : Measurable (im : π β β) :=
continuous_im.Measurable
#align is_R_or_C.measurable_im IsROrC.measurable_im
+-/
end IsROrC
@@ -44,29 +48,33 @@ section IsROrCComposition
variable {Ξ± π : Type _} [IsROrC π] {m : MeasurableSpace Ξ±} {f : Ξ± β π} {ΞΌ : MeasureTheory.Measure Ξ±}
-include m
-
+#print Measurable.re /-
@[measurability]
theorem Measurable.re (hf : Measurable f) : Measurable fun x => IsROrC.re (f x) :=
IsROrC.measurable_re.comp hf
#align measurable.re Measurable.re
+-/
+#print AEMeasurable.re /-
@[measurability]
theorem AEMeasurable.re (hf : AEMeasurable f ΞΌ) : AEMeasurable (fun x => IsROrC.re (f x)) ΞΌ :=
IsROrC.measurable_re.comp_aemeasurable hf
#align ae_measurable.re AEMeasurable.re
+-/
+#print Measurable.im /-
@[measurability]
theorem Measurable.im (hf : Measurable f) : Measurable fun x => IsROrC.im (f x) :=
IsROrC.measurable_im.comp hf
#align measurable.im Measurable.im
+-/
+#print AEMeasurable.im /-
@[measurability]
theorem AEMeasurable.im (hf : AEMeasurable f ΞΌ) : AEMeasurable (fun x => IsROrC.im (f x)) ΞΌ :=
IsROrC.measurable_im.comp_aemeasurable hf
#align ae_measurable.im AEMeasurable.im
-
-omit m
+-/
end IsROrCComposition
@@ -81,6 +89,7 @@ theorem IsROrC.measurable_ofReal : Measurable (coe : β β π) :=
#align is_R_or_C.measurable_of_real IsROrC.measurable_ofReal
-/
+#print measurable_of_re_im /-
theorem measurable_of_re_im (hre : Measurable fun x => IsROrC.re (f x))
(him : Measurable fun x => IsROrC.im (f x)) : Measurable f :=
by
@@ -91,7 +100,9 @@ theorem measurable_of_re_im (hre : Measurable fun x => IsROrC.re (f x))
exact (IsROrC.re_add_im _).symm
all_goals infer_instance
#align measurable_of_re_im measurable_of_re_im
+-/
+#print aemeasurable_of_re_im /-
theorem aemeasurable_of_re_im (hre : AEMeasurable (fun x => IsROrC.re (f x)) ΞΌ)
(him : AEMeasurable (fun x => IsROrC.im (f x)) ΞΌ) : AEMeasurable f ΞΌ :=
by
@@ -102,6 +113,7 @@ theorem aemeasurable_of_re_im (hre : AEMeasurable (fun x => IsROrC.re (f x)) ΞΌ)
exact (IsROrC.re_add_im _).symm
all_goals infer_instance
#align ae_measurable_of_re_im aemeasurable_of_re_im
+-/
end
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -84,7 +84,8 @@ theorem IsROrC.measurable_ofReal : Measurable (coe : β β π) :=
theorem measurable_of_re_im (hre : Measurable fun x => IsROrC.re (f x))
(him : Measurable fun x => IsROrC.im (f x)) : Measurable f :=
by
- convert(is_R_or_C.measurable_of_real.comp hre).add
+ convert
+ (is_R_or_C.measurable_of_real.comp hre).add
((is_R_or_C.measurable_of_real.comp him).mul_const IsROrC.i)
Β· ext1 x
exact (IsROrC.re_add_im _).symm
@@ -94,7 +95,8 @@ theorem measurable_of_re_im (hre : Measurable fun x => IsROrC.re (f x))
theorem aemeasurable_of_re_im (hre : AEMeasurable (fun x => IsROrC.re (f x)) ΞΌ)
(him : AEMeasurable (fun x => IsROrC.im (f x)) ΞΌ) : AEMeasurable f ΞΌ :=
by
- convert(is_R_or_C.measurable_of_real.comp_ae_measurable hre).add
+ convert
+ (is_R_or_C.measurable_of_real.comp_ae_measurable hre).add
((is_R_or_C.measurable_of_real.comp_ae_measurable him).mul_const IsROrC.i)
Β· ext1 x
exact (IsROrC.re_add_im _).symm
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -22,7 +22,7 @@ import Mathbin.Data.IsROrC.Lemmas
noncomputable section
-open NNReal ENNReal
+open scoped NNReal ENNReal
namespace IsROrC
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -28,23 +28,11 @@ namespace IsROrC
variable {π : Type _} [IsROrC π]
-/- warning: is_R_or_C.measurable_re -> IsROrC.measurable_re is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : IsROrC.{u1} π], Measurable.{u1, 0} π Real (IsROrC.measurableSpace.{u1} π _inst_1) Real.measurableSpace (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddMonoidWithOne.toAddMonoid.{u1} π (AddGroupWithOne.toAddMonoidWithOne.{u1} π (AddCommGroupWithOne.toAddGroupWithOne.{u1} π (Ring.toAddCommGroupWithOne.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddMonoidWithOne.toAddMonoid.{u1} π (AddGroupWithOne.toAddMonoidWithOne.{u1} π (AddCommGroupWithOne.toAddGroupWithOne.{u1} π (Ring.toAddCommGroupWithOne.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => π -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddMonoidWithOne.toAddMonoid.{u1} π (AddGroupWithOne.toAddMonoidWithOne.{u1} π (AddCommGroupWithOne.toAddGroupWithOne.{u1} π (Ring.toAddCommGroupWithOne.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} π _inst_1))
-but is expected to have type
- forall {π : Type.{u1}} [_inst_1 : IsROrC.{u1} π], Measurable.{u1, 0} π Real (IsROrC.measurableSpace.{u1} π _inst_1) Real.measurableSpace (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))
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.measurable_re IsROrC.measurable_reβ'. -/
@[measurability]
theorem measurable_re : Measurable (re : π β β) :=
continuous_re.Measurable
#align is_R_or_C.measurable_re IsROrC.measurable_re
-/- warning: is_R_or_C.measurable_im -> IsROrC.measurable_im is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : IsROrC.{u1} π], Measurable.{u1, 0} π Real (IsROrC.measurableSpace.{u1} π _inst_1) Real.measurableSpace (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddMonoidWithOne.toAddMonoid.{u1} π (AddGroupWithOne.toAddMonoidWithOne.{u1} π (AddCommGroupWithOne.toAddGroupWithOne.{u1} π (Ring.toAddCommGroupWithOne.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddMonoidWithOne.toAddMonoid.{u1} π (AddGroupWithOne.toAddMonoidWithOne.{u1} π (AddCommGroupWithOne.toAddGroupWithOne.{u1} π (Ring.toAddCommGroupWithOne.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => π -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddMonoidWithOne.toAddMonoid.{u1} π (AddGroupWithOne.toAddMonoidWithOne.{u1} π (AddCommGroupWithOne.toAddGroupWithOne.{u1} π (Ring.toAddCommGroupWithOne.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} π _inst_1))
-but is expected to have type
- forall {π : Type.{u1}} [_inst_1 : IsROrC.{u1} π], Measurable.{u1, 0} π Real (IsROrC.measurableSpace.{u1} π _inst_1) Real.measurableSpace (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))
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.measurable_im IsROrC.measurable_imβ'. -/
@[measurability]
theorem measurable_im : Measurable (im : π β β) :=
continuous_im.Measurable
@@ -58,33 +46,21 @@ variable {Ξ± π : Type _} [IsROrC π] {m : MeasurableSpace Ξ±} {f : Ξ± β
include m
-/- warning: measurable.re -> Measurable.re is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align measurable.re Measurable.reβ'. -/
@[measurability]
theorem Measurable.re (hf : Measurable f) : Measurable fun x => IsROrC.re (f x) :=
IsROrC.measurable_re.comp hf
#align measurable.re Measurable.re
-/- warning: ae_measurable.re -> AEMeasurable.re is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ae_measurable.re AEMeasurable.reβ'. -/
@[measurability]
theorem AEMeasurable.re (hf : AEMeasurable f ΞΌ) : AEMeasurable (fun x => IsROrC.re (f x)) ΞΌ :=
IsROrC.measurable_re.comp_aemeasurable hf
#align ae_measurable.re AEMeasurable.re
-/- warning: measurable.im -> Measurable.im is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align measurable.im Measurable.imβ'. -/
@[measurability]
theorem Measurable.im (hf : Measurable f) : Measurable fun x => IsROrC.im (f x) :=
IsROrC.measurable_im.comp hf
#align measurable.im Measurable.im
-/- warning: ae_measurable.im -> AEMeasurable.im is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ae_measurable.im AEMeasurable.imβ'. -/
@[measurability]
theorem AEMeasurable.im (hf : AEMeasurable f ΞΌ) : AEMeasurable (fun x => IsROrC.im (f x)) ΞΌ :=
IsROrC.measurable_im.comp_aemeasurable hf
@@ -105,9 +81,6 @@ theorem IsROrC.measurable_ofReal : Measurable (coe : β β π) :=
#align is_R_or_C.measurable_of_real IsROrC.measurable_ofReal
-/
-/- warning: measurable_of_re_im -> measurable_of_re_im is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align measurable_of_re_im measurable_of_re_imβ'. -/
theorem measurable_of_re_im (hre : Measurable fun x => IsROrC.re (f x))
(him : Measurable fun x => IsROrC.im (f x)) : Measurable f :=
by
@@ -118,9 +91,6 @@ theorem measurable_of_re_im (hre : Measurable fun x => IsROrC.re (f x))
all_goals infer_instance
#align measurable_of_re_im measurable_of_re_im
-/- warning: ae_measurable_of_re_im -> aemeasurable_of_re_im is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ae_measurable_of_re_im aemeasurable_of_re_imβ'. -/
theorem aemeasurable_of_re_im (hre : AEMeasurable (fun x => IsROrC.re (f x)) ΞΌ)
(him : AEMeasurable (fun x => IsROrC.im (f x)) ΞΌ) : AEMeasurable f ΞΌ :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -59,10 +59,7 @@ variable {Ξ± π : Type _} [IsROrC π] {m : MeasurableSpace Ξ±} {f : Ξ± β
include m
/- warning: measurable.re -> Measurable.re is a dubious translation:
-lean 3 declaration is
- forall {Ξ± : Type.{u1}} {π : Type.{u2}} [_inst_1 : IsROrC.{u2} π] {m : MeasurableSpace.{u1} Ξ±} {f : Ξ± -> π}, (Measurable.{u1, u2} Ξ± π m (IsROrC.measurableSpace.{u2} π _inst_1) f) -> (Measurable.{u1, 0} Ξ± Real m Real.measurableSpace (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)))
-but is expected to have type
- forall {Ξ± : Type.{u2}} {π : Type.{u1}} [_inst_1 : IsROrC.{u1} π] {m : MeasurableSpace.{u2} Ξ±} {f : Ξ± -> π}, (Measurable.{u2, u1} Ξ± π m (IsROrC.measurableSpace.{u1} π _inst_1) f) -> (Measurable.{u2, 0} Ξ± Real m Real.measurableSpace (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)))
+<too large>
Case conversion may be inaccurate. Consider using '#align measurable.re Measurable.reβ'. -/
@[measurability]
theorem Measurable.re (hf : Measurable f) : Measurable fun x => IsROrC.re (f x) :=
@@ -70,10 +67,7 @@ theorem Measurable.re (hf : Measurable f) : Measurable fun x => IsROrC.re (f x)
#align measurable.re Measurable.re
/- warning: ae_measurable.re -> AEMeasurable.re is a dubious translation:
-lean 3 declaration is
- forall {Ξ± : Type.{u1}} {π : Type.{u2}} [_inst_1 : IsROrC.{u2} π] {m : MeasurableSpace.{u1} Ξ±} {f : Ξ± -> π} {ΞΌ : MeasureTheory.Measure.{u1} Ξ± m}, (AEMeasurable.{u1, u2} Ξ± π (IsROrC.measurableSpace.{u2} π _inst_1) m f ΞΌ) -> (AEMeasurable.{u1, 0} Ξ± Real Real.measurableSpace 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}} {π : Type.{u1}} [_inst_1 : IsROrC.{u1} π] {m : MeasurableSpace.{u2} Ξ±} {f : Ξ± -> π} {ΞΌ : MeasureTheory.Measure.{u2} Ξ± m}, (AEMeasurable.{u2, u1} Ξ± π (IsROrC.measurableSpace.{u1} π _inst_1) m f ΞΌ) -> (AEMeasurable.{u2, 0} Ξ± Real Real.measurableSpace 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 ae_measurable.re AEMeasurable.reβ'. -/
@[measurability]
theorem AEMeasurable.re (hf : AEMeasurable f ΞΌ) : AEMeasurable (fun x => IsROrC.re (f x)) ΞΌ :=
@@ -81,10 +75,7 @@ theorem AEMeasurable.re (hf : AEMeasurable f ΞΌ) : AEMeasurable (fun x => IsROrC
#align ae_measurable.re AEMeasurable.re
/- warning: measurable.im -> Measurable.im is a dubious translation:
-lean 3 declaration is
- forall {Ξ± : Type.{u1}} {π : Type.{u2}} [_inst_1 : IsROrC.{u2} π] {m : MeasurableSpace.{u1} Ξ±} {f : Ξ± -> π}, (Measurable.{u1, u2} Ξ± π m (IsROrC.measurableSpace.{u2} π _inst_1) f) -> (Measurable.{u1, 0} Ξ± Real m Real.measurableSpace (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)))
-but is expected to have type
- forall {Ξ± : Type.{u2}} {π : Type.{u1}} [_inst_1 : IsROrC.{u1} π] {m : MeasurableSpace.{u2} Ξ±} {f : Ξ± -> π}, (Measurable.{u2, u1} Ξ± π m (IsROrC.measurableSpace.{u1} π _inst_1) f) -> (Measurable.{u2, 0} Ξ± Real m Real.measurableSpace (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)))
+<too large>
Case conversion may be inaccurate. Consider using '#align measurable.im Measurable.imβ'. -/
@[measurability]
theorem Measurable.im (hf : Measurable f) : Measurable fun x => IsROrC.im (f x) :=
@@ -92,10 +83,7 @@ theorem Measurable.im (hf : Measurable f) : Measurable fun x => IsROrC.im (f x)
#align measurable.im Measurable.im
/- warning: ae_measurable.im -> AEMeasurable.im is a dubious translation:
-lean 3 declaration is
- forall {Ξ± : Type.{u1}} {π : Type.{u2}} [_inst_1 : IsROrC.{u2} π] {m : MeasurableSpace.{u1} Ξ±} {f : Ξ± -> π} {ΞΌ : MeasureTheory.Measure.{u1} Ξ± m}, (AEMeasurable.{u1, u2} Ξ± π (IsROrC.measurableSpace.{u2} π _inst_1) m f ΞΌ) -> (AEMeasurable.{u1, 0} Ξ± Real Real.measurableSpace 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}} {π : Type.{u1}} [_inst_1 : IsROrC.{u1} π] {m : MeasurableSpace.{u2} Ξ±} {f : Ξ± -> π} {ΞΌ : MeasureTheory.Measure.{u2} Ξ± m}, (AEMeasurable.{u2, u1} Ξ± π (IsROrC.measurableSpace.{u1} π _inst_1) m f ΞΌ) -> (AEMeasurable.{u2, 0} Ξ± Real Real.measurableSpace 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 ae_measurable.im AEMeasurable.imβ'. -/
@[measurability]
theorem AEMeasurable.im (hf : AEMeasurable f ΞΌ) : AEMeasurable (fun x => IsROrC.im (f x)) ΞΌ :=
@@ -110,18 +98,15 @@ section
variable {Ξ± π : Type _} [IsROrC π] [MeasurableSpace Ξ±] {f : Ξ± β π} {ΞΌ : MeasureTheory.Measure Ξ±}
-#print IsROrC.measurable_of_real /-
+#print IsROrC.measurable_ofReal /-
@[measurability]
-theorem IsROrC.measurable_of_real : Measurable (coe : β β π) :=
+theorem IsROrC.measurable_ofReal : Measurable (coe : β β π) :=
IsROrC.continuous_ofReal.Measurable
-#align is_R_or_C.measurable_of_real IsROrC.measurable_of_real
+#align is_R_or_C.measurable_of_real IsROrC.measurable_ofReal
-/
/- warning: measurable_of_re_im -> measurable_of_re_im is a dubious translation:
-lean 3 declaration is
- forall {Ξ± : Type.{u1}} {π : Type.{u2}} [_inst_1 : IsROrC.{u2} π] [_inst_2 : MeasurableSpace.{u1} Ξ±] {f : Ξ± -> π}, (Measurable.{u1, 0} Ξ± Real _inst_2 Real.measurableSpace (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))) -> (Measurable.{u1, 0} Ξ± Real _inst_2 Real.measurableSpace (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))) -> (Measurable.{u1, u2} Ξ± π _inst_2 (IsROrC.measurableSpace.{u2} π _inst_1) f)
-but is expected to have type
- forall {Ξ± : Type.{u2}} {π : Type.{u1}} [_inst_1 : IsROrC.{u1} π] [_inst_2 : MeasurableSpace.{u2} Ξ±] {f : Ξ± -> π}, (Measurable.{u2, 0} Ξ± Real _inst_2 Real.measurableSpace (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))) -> (Measurable.{u2, 0} Ξ± Real _inst_2 Real.measurableSpace (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))) -> (Measurable.{u2, u1} Ξ± π _inst_2 (IsROrC.measurableSpace.{u1} π _inst_1) f)
+<too large>
Case conversion may be inaccurate. Consider using '#align measurable_of_re_im measurable_of_re_imβ'. -/
theorem measurable_of_re_im (hre : Measurable fun x => IsROrC.re (f x))
(him : Measurable fun x => IsROrC.im (f x)) : Measurable f :=
@@ -134,10 +119,7 @@ theorem measurable_of_re_im (hre : Measurable fun x => IsROrC.re (f x))
#align measurable_of_re_im measurable_of_re_im
/- warning: ae_measurable_of_re_im -> aemeasurable_of_re_im is a dubious translation:
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-but is expected to have type
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(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) -> (AEMeasurable.{u2, 0} Ξ± Real Real.measurableSpace _inst_2 (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) -> (AEMeasurable.{u2, u1} Ξ± π (IsROrC.measurableSpace.{u1} π _inst_1) _inst_2 f ΞΌ)
+<too large>
Case conversion may be inaccurate. Consider using '#align ae_measurable_of_re_im aemeasurable_of_re_imβ'. -/
theorem aemeasurable_of_re_im (hre : AEMeasurable (fun x => IsROrC.re (f x)) ΞΌ)
(him : AEMeasurable (fun x => IsROrC.im (f x)) ΞΌ) : AEMeasurable f ΞΌ :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
! This file was ported from Lean 3 source module measure_theory.function.special_functions.is_R_or_C
-! leanprover-community/mathlib commit 83a66c8775fa14ee5180c85cab98e970956401ad
+! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.Data.IsROrC.Lemmas
/-!
# Measurability of the basic `is_R_or_C` functions
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828
@@ -25,11 +25,23 @@ namespace IsROrC
variable {π : Type _} [IsROrC π]
+/- warning: is_R_or_C.measurable_re -> IsROrC.measurable_re is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : IsROrC.{u1} π], Measurable.{u1, 0} π Real (IsROrC.measurableSpace.{u1} π _inst_1) Real.measurableSpace (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddMonoidWithOne.toAddMonoid.{u1} π (AddGroupWithOne.toAddMonoidWithOne.{u1} π (AddCommGroupWithOne.toAddGroupWithOne.{u1} π (Ring.toAddCommGroupWithOne.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddMonoidWithOne.toAddMonoid.{u1} π (AddGroupWithOne.toAddMonoidWithOne.{u1} π (AddCommGroupWithOne.toAddGroupWithOne.{u1} π (Ring.toAddCommGroupWithOne.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => π -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddMonoidWithOne.toAddMonoid.{u1} π (AddGroupWithOne.toAddMonoidWithOne.{u1} π (AddCommGroupWithOne.toAddGroupWithOne.{u1} π (Ring.toAddCommGroupWithOne.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} π _inst_1))
+but is expected to have type
+ forall {π : Type.{u1}} [_inst_1 : IsROrC.{u1} π], Measurable.{u1, 0} π Real (IsROrC.measurableSpace.{u1} π _inst_1) Real.measurableSpace (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))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.measurable_re IsROrC.measurable_reβ'. -/
@[measurability]
theorem measurable_re : Measurable (re : π β β) :=
continuous_re.Measurable
#align is_R_or_C.measurable_re IsROrC.measurable_re
+/- warning: is_R_or_C.measurable_im -> IsROrC.measurable_im is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : IsROrC.{u1} π], Measurable.{u1, 0} π Real (IsROrC.measurableSpace.{u1} π _inst_1) Real.measurableSpace (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddMonoidWithOne.toAddMonoid.{u1} π (AddGroupWithOne.toAddMonoidWithOne.{u1} π (AddCommGroupWithOne.toAddGroupWithOne.{u1} π (Ring.toAddCommGroupWithOne.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddMonoidWithOne.toAddMonoid.{u1} π (AddGroupWithOne.toAddMonoidWithOne.{u1} π (AddCommGroupWithOne.toAddGroupWithOne.{u1} π (Ring.toAddCommGroupWithOne.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => π -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} π Real (AddMonoid.toAddZeroClass.{u1} π (AddMonoidWithOne.toAddMonoid.{u1} π (AddGroupWithOne.toAddMonoidWithOne.{u1} π (AddCommGroupWithOne.toAddGroupWithOne.{u1} π (Ring.toAddCommGroupWithOne.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (DenselyNormedField.toNormedField.{u1} π (IsROrC.toDenselyNormedField.{u1} π _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} π _inst_1))
+but is expected to have type
+ forall {π : Type.{u1}} [_inst_1 : IsROrC.{u1} π], Measurable.{u1, 0} π Real (IsROrC.measurableSpace.{u1} π _inst_1) Real.measurableSpace (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))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.measurable_im IsROrC.measurable_imβ'. -/
@[measurability]
theorem measurable_im : Measurable (im : π β β) :=
continuous_im.Measurable
@@ -43,21 +55,45 @@ variable {Ξ± π : Type _} [IsROrC π] {m : MeasurableSpace Ξ±} {f : Ξ± β
include m
+/- warning: measurable.re -> Measurable.re is a dubious translation:
+lean 3 declaration is
+ forall {Ξ± : Type.{u1}} {π : Type.{u2}} [_inst_1 : IsROrC.{u2} π] {m : MeasurableSpace.{u1} Ξ±} {f : Ξ± -> π}, (Measurable.{u1, u2} Ξ± π m (IsROrC.measurableSpace.{u2} π _inst_1) f) -> (Measurable.{u1, 0} Ξ± Real m Real.measurableSpace (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)))
+but is expected to have type
+ forall {Ξ± : Type.{u2}} {π : Type.{u1}} [_inst_1 : IsROrC.{u1} π] {m : MeasurableSpace.{u2} Ξ±} {f : Ξ± -> π}, (Measurable.{u2, u1} Ξ± π m (IsROrC.measurableSpace.{u1} π _inst_1) f) -> (Measurable.{u2, 0} Ξ± Real m Real.measurableSpace (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)))
+Case conversion may be inaccurate. Consider using '#align measurable.re Measurable.reβ'. -/
@[measurability]
theorem Measurable.re (hf : Measurable f) : Measurable fun x => IsROrC.re (f x) :=
IsROrC.measurable_re.comp hf
#align measurable.re Measurable.re
+/- warning: ae_measurable.re -> AEMeasurable.re is a dubious translation:
+lean 3 declaration is
+ forall {Ξ± : Type.{u1}} {π : Type.{u2}} [_inst_1 : IsROrC.{u2} π] {m : MeasurableSpace.{u1} Ξ±} {f : Ξ± -> π} {ΞΌ : MeasureTheory.Measure.{u1} Ξ± m}, (AEMeasurable.{u1, u2} Ξ± π (IsROrC.measurableSpace.{u2} π _inst_1) m f ΞΌ) -> (AEMeasurable.{u1, 0} Ξ± Real Real.measurableSpace 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}} {π : Type.{u1}} [_inst_1 : IsROrC.{u1} π] {m : MeasurableSpace.{u2} Ξ±} {f : Ξ± -> π} {ΞΌ : MeasureTheory.Measure.{u2} Ξ± m}, (AEMeasurable.{u2, u1} Ξ± π (IsROrC.measurableSpace.{u1} π _inst_1) m f ΞΌ) -> (AEMeasurable.{u2, 0} Ξ± Real Real.measurableSpace 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 ae_measurable.re AEMeasurable.reβ'. -/
@[measurability]
theorem AEMeasurable.re (hf : AEMeasurable f ΞΌ) : AEMeasurable (fun x => IsROrC.re (f x)) ΞΌ :=
IsROrC.measurable_re.comp_aemeasurable hf
#align ae_measurable.re AEMeasurable.re
+/- warning: measurable.im -> Measurable.im is a dubious translation:
+lean 3 declaration is
+ forall {Ξ± : Type.{u1}} {π : Type.{u2}} [_inst_1 : IsROrC.{u2} π] {m : MeasurableSpace.{u1} Ξ±} {f : Ξ± -> π}, (Measurable.{u1, u2} Ξ± π m (IsROrC.measurableSpace.{u2} π _inst_1) f) -> (Measurable.{u1, 0} Ξ± Real m Real.measurableSpace (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)))
+but is expected to have type
+ forall {Ξ± : Type.{u2}} {π : Type.{u1}} [_inst_1 : IsROrC.{u1} π] {m : MeasurableSpace.{u2} Ξ±} {f : Ξ± -> π}, (Measurable.{u2, u1} Ξ± π m (IsROrC.measurableSpace.{u1} π _inst_1) f) -> (Measurable.{u2, 0} Ξ± Real m Real.measurableSpace (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)))
+Case conversion may be inaccurate. Consider using '#align measurable.im Measurable.imβ'. -/
@[measurability]
theorem Measurable.im (hf : Measurable f) : Measurable fun x => IsROrC.im (f x) :=
IsROrC.measurable_im.comp hf
#align measurable.im Measurable.im
+/- warning: ae_measurable.im -> AEMeasurable.im is a dubious translation:
+lean 3 declaration is
+ forall {Ξ± : Type.{u1}} {π : Type.{u2}} [_inst_1 : IsROrC.{u2} π] {m : MeasurableSpace.{u1} Ξ±} {f : Ξ± -> π} {ΞΌ : MeasureTheory.Measure.{u1} Ξ± m}, (AEMeasurable.{u1, u2} Ξ± π (IsROrC.measurableSpace.{u2} π _inst_1) m f ΞΌ) -> (AEMeasurable.{u1, 0} Ξ± Real Real.measurableSpace 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}} {π : Type.{u1}} [_inst_1 : IsROrC.{u1} π] {m : MeasurableSpace.{u2} Ξ±} {f : Ξ± -> π} {ΞΌ : MeasureTheory.Measure.{u2} Ξ± m}, (AEMeasurable.{u2, u1} Ξ± π (IsROrC.measurableSpace.{u1} π _inst_1) m f ΞΌ) -> (AEMeasurable.{u2, 0} Ξ± Real Real.measurableSpace 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 ae_measurable.im AEMeasurable.imβ'. -/
@[measurability]
theorem AEMeasurable.im (hf : AEMeasurable f ΞΌ) : AEMeasurable (fun x => IsROrC.im (f x)) ΞΌ :=
IsROrC.measurable_im.comp_aemeasurable hf
@@ -71,11 +107,19 @@ section
variable {Ξ± π : Type _} [IsROrC π] [MeasurableSpace Ξ±] {f : Ξ± β π} {ΞΌ : MeasureTheory.Measure Ξ±}
+#print IsROrC.measurable_of_real /-
@[measurability]
theorem IsROrC.measurable_of_real : Measurable (coe : β β π) :=
IsROrC.continuous_ofReal.Measurable
#align is_R_or_C.measurable_of_real IsROrC.measurable_of_real
+-/
+/- warning: measurable_of_re_im -> measurable_of_re_im is a dubious translation:
+lean 3 declaration is
+ forall {Ξ± : Type.{u1}} {π : Type.{u2}} [_inst_1 : IsROrC.{u2} π] [_inst_2 : MeasurableSpace.{u1} Ξ±] {f : Ξ± -> π}, (Measurable.{u1, 0} Ξ± Real _inst_2 Real.measurableSpace (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))) -> (Measurable.{u1, 0} Ξ± Real _inst_2 Real.measurableSpace (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))) -> (Measurable.{u1, u2} Ξ± π _inst_2 (IsROrC.measurableSpace.{u2} π _inst_1) f)
+but is expected to have type
+ forall {Ξ± : Type.{u2}} {π : Type.{u1}} [_inst_1 : IsROrC.{u1} π] [_inst_2 : MeasurableSpace.{u2} Ξ±] {f : Ξ± -> π}, (Measurable.{u2, 0} Ξ± Real _inst_2 Real.measurableSpace (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))) -> (Measurable.{u2, 0} Ξ± Real _inst_2 Real.measurableSpace (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))) -> (Measurable.{u2, u1} Ξ± π _inst_2 (IsROrC.measurableSpace.{u1} π _inst_1) f)
+Case conversion may be inaccurate. Consider using '#align measurable_of_re_im measurable_of_re_imβ'. -/
theorem measurable_of_re_im (hre : Measurable fun x => IsROrC.re (f x))
(him : Measurable fun x => IsROrC.im (f x)) : Measurable f :=
by
@@ -86,7 +130,13 @@ theorem measurable_of_re_im (hre : Measurable fun x => IsROrC.re (f x))
all_goals infer_instance
#align measurable_of_re_im measurable_of_re_im
-theorem aEMeasurable_of_re_im (hre : AEMeasurable (fun x => IsROrC.re (f x)) ΞΌ)
+/- warning: ae_measurable_of_re_im -> aemeasurable_of_re_im is a dubious translation:
+lean 3 declaration is
+ forall {Ξ± : Type.{u1}} {π : Type.{u2}} [_inst_1 : IsROrC.{u2} π] [_inst_2 : MeasurableSpace.{u1} Ξ±] {f : Ξ± -> π} {ΞΌ : MeasureTheory.Measure.{u1} Ξ± _inst_2}, (AEMeasurable.{u1, 0} Ξ± Real Real.measurableSpace _inst_2 (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) -> (AEMeasurable.{u1, 0} Ξ± Real Real.measurableSpace _inst_2 (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) -> (AEMeasurable.{u1, u2} Ξ± π (IsROrC.measurableSpace.{u2} π _inst_1) _inst_2 f ΞΌ)
+but is expected to have type
+ forall {Ξ± : Type.{u2}} {π : Type.{u1}} [_inst_1 : IsROrC.{u1} π] [_inst_2 : MeasurableSpace.{u2} Ξ±] {f : Ξ± -> π} {ΞΌ : MeasureTheory.Measure.{u2} Ξ± _inst_2}, (AEMeasurable.{u2, 0} Ξ± Real Real.measurableSpace _inst_2 (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) -> (AEMeasurable.{u2, 0} Ξ± Real Real.measurableSpace _inst_2 (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) -> (AEMeasurable.{u2, u1} Ξ± π (IsROrC.measurableSpace.{u1} π _inst_1) _inst_2 f ΞΌ)
+Case conversion may be inaccurate. Consider using '#align ae_measurable_of_re_im aemeasurable_of_re_imβ'. -/
+theorem aemeasurable_of_re_im (hre : AEMeasurable (fun x => IsROrC.re (f x)) ΞΌ)
(him : AEMeasurable (fun x => IsROrC.im (f x)) ΞΌ) : AEMeasurable f ΞΌ :=
by
convert(is_R_or_C.measurable_of_real.comp_ae_measurable hre).add
@@ -94,7 +144,7 @@ theorem aEMeasurable_of_re_im (hre : AEMeasurable (fun x => IsROrC.re (f x)) ΞΌ)
Β· ext1 x
exact (IsROrC.re_add_im _).symm
all_goals infer_instance
-#align ae_measurable_of_re_im aEMeasurable_of_re_im
+#align ae_measurable_of_re_im aemeasurable_of_re_im
end
mathlib commit https://github.com/leanprover-community/mathlib/commit/f51de8769c34652d82d1c8e5f8f18f8374782bed
Data
(#11753)
RCLike
is an analytic typeclass, hence should be under Analysis
@@ -3,7 +3,7 @@ Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
-import Mathlib.Data.RCLike.Lemmas
+import Mathlib.Analysis.RCLike.Lemmas
import Mathlib.MeasureTheory.Constructions.BorelSpace.Complex
#align_import measure_theory.function.special_functions.is_R_or_C from "leanprover-community/mathlib"@"83a66c8775fa14ee5180c85cab98e970956401ad"
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
.
@@ -3,8 +3,8 @@ Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
-import Mathlib.MeasureTheory.Function.SpecialFunctions.Basic
import Mathlib.Data.IsROrC.Lemmas
+import Mathlib.MeasureTheory.Constructions.BorelSpace.Complex
#align_import measure_theory.function.special_functions.is_R_or_C from "leanprover-community/mathlib"@"83a66c8775fa14ee5180c85cab98e970956401ad"
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -20,7 +20,7 @@ open NNReal ENNReal
namespace IsROrC
-variable {π : Type _} [IsROrC π]
+variable {π : Type*} [IsROrC π]
@[measurability]
theorem measurable_re : Measurable (re : π β β) :=
@@ -36,7 +36,7 @@ end IsROrC
section IsROrCComposition
-variable {Ξ± π : Type _} [IsROrC π] {m : MeasurableSpace Ξ±} {f : Ξ± β π} {ΞΌ : MeasureTheory.Measure Ξ±}
+variable {Ξ± π : Type*} [IsROrC π] {m : MeasurableSpace Ξ±} {f : Ξ± β π} {ΞΌ : MeasureTheory.Measure Ξ±}
@[measurability]
theorem Measurable.re (hf : Measurable f) : Measurable fun x => IsROrC.re (f x) :=
@@ -62,7 +62,7 @@ end IsROrCComposition
section
-variable {Ξ± π : Type _} [IsROrC π] [MeasurableSpace Ξ±] {f : Ξ± β π} {ΞΌ : MeasureTheory.Measure Ξ±}
+variable {Ξ± π : Type*} [IsROrC π] [MeasurableSpace Ξ±] {f : Ξ± β π} {ΞΌ : MeasureTheory.Measure Ξ±}
@[measurability]
theorem IsROrC.measurable_ofReal : Measurable ((β) : β β π) :=
@@ -2,15 +2,12 @@
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module measure_theory.function.special_functions.is_R_or_C
-! leanprover-community/mathlib commit 83a66c8775fa14ee5180c85cab98e970956401ad
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.MeasureTheory.Function.SpecialFunctions.Basic
import Mathlib.Data.IsROrC.Lemmas
+#align_import measure_theory.function.special_functions.is_R_or_C from "leanprover-community/mathlib"@"83a66c8775fa14ee5180c85cab98e970956401ad"
+
/-!
# Measurability of the basic `IsROrC` functions
@@ -68,21 +68,21 @@ section
variable {Ξ± π : Type _} [IsROrC π] [MeasurableSpace Ξ±] {f : Ξ± β π} {ΞΌ : MeasureTheory.Measure Ξ±}
@[measurability]
-theorem IsROrC.measurable_of_real : Measurable ((β) : β β π) :=
+theorem IsROrC.measurable_ofReal : Measurable ((β) : β β π) :=
IsROrC.continuous_ofReal.measurable
-#align is_R_or_C.measurable_of_real IsROrC.measurable_of_real
+#align is_R_or_C.measurable_of_real IsROrC.measurable_ofReal
theorem measurable_of_re_im (hre : Measurable fun x => IsROrC.re (f x))
(him : Measurable fun x => IsROrC.im (f x)) : Measurable f := by
- convert Measurable.add (M := π) (IsROrC.measurable_of_real.comp hre)
- ((IsROrC.measurable_of_real.comp him).mul_const IsROrC.I)
+ convert Measurable.add (M := π) (IsROrC.measurable_ofReal.comp hre)
+ ((IsROrC.measurable_ofReal.comp him).mul_const IsROrC.I)
exact (IsROrC.re_add_im _).symm
#align measurable_of_re_im measurable_of_re_im
theorem aemeasurable_of_re_im (hre : AEMeasurable (fun x => IsROrC.re (f x)) ΞΌ)
(him : AEMeasurable (fun x => IsROrC.im (f x)) ΞΌ) : AEMeasurable f ΞΌ := by
- convert AEMeasurable.add (M := π) (IsROrC.measurable_of_real.comp_aemeasurable hre)
- ((IsROrC.measurable_of_real.comp_aemeasurable him).mul_const IsROrC.I)
+ convert AEMeasurable.add (M := π) (IsROrC.measurable_ofReal.comp_aemeasurable hre)
+ ((IsROrC.measurable_ofReal.comp_aemeasurable him).mul_const IsROrC.I)
exact (IsROrC.re_add_im _).symm
#align ae_measurable_of_re_im aemeasurable_of_re_im
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