measure_theory.function.floor
⟷
Mathlib.MeasureTheory.Function.Floor
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/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,7 +3,7 @@ Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
-import Mathbin.MeasureTheory.Constructions.BorelSpace.Basic
+import MeasureTheory.Constructions.BorelSpace.Basic
#align_import measure_theory.function.floor from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-
-! This file was ported from Lean 3 source module measure_theory.function.floor
-! leanprover-community/mathlib commit 4280f5f32e16755ec7985ce11e189b6cd6ff6735
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.MeasureTheory.Constructions.BorelSpace.Basic
+#align_import measure_theory.function.floor from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"
+
/-!
# Measurability of `⌊x⌋` etc
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -98,10 +98,12 @@ theorem Nat.measurable_floor : Measurable (Nat.floor : R → ℕ) :=
#align nat.measurable_floor Nat.measurable_floor
-/
+#print Measurable.nat_floor /-
@[measurability]
theorem Measurable.nat_floor (hf : Measurable f) : Measurable fun x => ⌊f x⌋₊ :=
Nat.measurable_floor.comp hf
#align measurable.nat_floor Measurable.nat_floor
+-/
#print Nat.measurable_ceil /-
theorem Nat.measurable_ceil : Measurable (Nat.ceil : R → ℕ) :=
@@ -110,10 +112,12 @@ theorem Nat.measurable_ceil : Measurable (Nat.ceil : R → ℕ) :=
#align nat.measurable_ceil Nat.measurable_ceil
-/
+#print Measurable.nat_ceil /-
@[measurability]
theorem Measurable.nat_ceil (hf : Measurable f) : Measurable fun x => ⌈f x⌉₊ :=
Nat.measurable_ceil.comp hf
#align measurable.nat_ceil Measurable.nat_ceil
+-/
end FloorSemiring
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -98,12 +98,6 @@ theorem Nat.measurable_floor : Measurable (Nat.floor : R → ℕ) :=
#align nat.measurable_floor Nat.measurable_floor
-/
-/- warning: measurable.nat_floor -> Measurable.nat_floor is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {R : Type.{u2}} [_inst_1 : MeasurableSpace.{u1} α] [_inst_2 : LinearOrderedSemiring.{u2} R] [_inst_3 : FloorSemiring.{u2} R (StrictOrderedSemiring.toOrderedSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R _inst_2))] [_inst_4 : TopologicalSpace.{u2} R] [_inst_5 : OrderTopology.{u2} R _inst_4 (PartialOrder.toPreorder.{u2} R (OrderedCancelAddCommMonoid.toPartialOrder.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R _inst_2))))] [_inst_6 : MeasurableSpace.{u2} R] [_inst_7 : OpensMeasurableSpace.{u2} R _inst_4 _inst_6] {f : α -> R}, (Measurable.{u1, u2} α R _inst_1 _inst_6 f) -> (Measurable.{u1, 0} α Nat _inst_1 Nat.instMeasurableSpace (fun (x : α) => Nat.floor.{u2} R (StrictOrderedSemiring.toOrderedSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R _inst_2)) _inst_3 (f x)))
-but is expected to have type
- forall {α : Type.{u2}} {R : Type.{u1}} [_inst_1 : MeasurableSpace.{u2} α] [_inst_2 : LinearOrderedSemiring.{u1} R] [_inst_3 : FloorSemiring.{u1} R (StrictOrderedSemiring.toOrderedSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R _inst_2))] [_inst_4 : TopologicalSpace.{u1} R] [_inst_5 : OrderTopology.{u1} R _inst_4 (PartialOrder.toPreorder.{u1} R (StrictOrderedSemiring.toPartialOrder.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R _inst_2)))] [_inst_6 : MeasurableSpace.{u1} R] [_inst_7 : OpensMeasurableSpace.{u1} R _inst_4 _inst_6] {f : α -> R}, (Measurable.{u2, u1} α R _inst_1 _inst_6 f) -> (Measurable.{u2, 0} α Nat _inst_1 Nat.instMeasurableSpace (fun (x : α) => Nat.floor.{u1} R (StrictOrderedSemiring.toOrderedSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R _inst_2)) _inst_3 (f x)))
-Case conversion may be inaccurate. Consider using '#align measurable.nat_floor Measurable.nat_floorₓ'. -/
@[measurability]
theorem Measurable.nat_floor (hf : Measurable f) : Measurable fun x => ⌊f x⌋₊ :=
Nat.measurable_floor.comp hf
@@ -116,12 +110,6 @@ theorem Nat.measurable_ceil : Measurable (Nat.ceil : R → ℕ) :=
#align nat.measurable_ceil Nat.measurable_ceil
-/
-/- warning: measurable.nat_ceil -> Measurable.nat_ceil is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {R : Type.{u2}} [_inst_1 : MeasurableSpace.{u1} α] [_inst_2 : LinearOrderedSemiring.{u2} R] [_inst_3 : FloorSemiring.{u2} R (StrictOrderedSemiring.toOrderedSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R _inst_2))] [_inst_4 : TopologicalSpace.{u2} R] [_inst_5 : OrderTopology.{u2} R _inst_4 (PartialOrder.toPreorder.{u2} R (OrderedCancelAddCommMonoid.toPartialOrder.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R _inst_2))))] [_inst_6 : MeasurableSpace.{u2} R] [_inst_7 : OpensMeasurableSpace.{u2} R _inst_4 _inst_6] {f : α -> R}, (Measurable.{u1, u2} α R _inst_1 _inst_6 f) -> (Measurable.{u1, 0} α Nat _inst_1 Nat.instMeasurableSpace (fun (x : α) => Nat.ceil.{u2} R (StrictOrderedSemiring.toOrderedSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R _inst_2)) _inst_3 (f x)))
-but is expected to have type
- forall {α : Type.{u2}} {R : Type.{u1}} [_inst_1 : MeasurableSpace.{u2} α] [_inst_2 : LinearOrderedSemiring.{u1} R] [_inst_3 : FloorSemiring.{u1} R (StrictOrderedSemiring.toOrderedSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R _inst_2))] [_inst_4 : TopologicalSpace.{u1} R] [_inst_5 : OrderTopology.{u1} R _inst_4 (PartialOrder.toPreorder.{u1} R (StrictOrderedSemiring.toPartialOrder.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R _inst_2)))] [_inst_6 : MeasurableSpace.{u1} R] [_inst_7 : OpensMeasurableSpace.{u1} R _inst_4 _inst_6] {f : α -> R}, (Measurable.{u2, u1} α R _inst_1 _inst_6 f) -> (Measurable.{u2, 0} α Nat _inst_1 Nat.instMeasurableSpace (fun (x : α) => Nat.ceil.{u1} R (StrictOrderedSemiring.toOrderedSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R _inst_2)) _inst_3 (f x)))
-Case conversion may be inaccurate. Consider using '#align measurable.nat_ceil Measurable.nat_ceilₓ'. -/
@[measurability]
theorem Measurable.nat_ceil (hf : Measurable f) : Measurable fun x => ⌈f x⌉₊ :=
Nat.measurable_ceil.comp hf
mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
! This file was ported from Lean 3 source module measure_theory.function.floor
-! leanprover-community/mathlib commit bf6a01357ff5684b1ebcd0f1a13be314fc82c0bf
+! leanprover-community/mathlib commit 4280f5f32e16755ec7985ce11e189b6cd6ff6735
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -13,6 +13,9 @@ import Mathbin.MeasureTheory.Constructions.BorelSpace.Basic
/-!
# Measurability of `⌊x⌋` etc
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
In this file we prove that `int.floor`, `int.ceil`, `int.fract`, `nat.floor`, and `nat.ceil` are
measurable under some assumptions on the (semi)ring.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952
@@ -25,47 +25,61 @@ section FloorRing
variable {α R : Type _} [MeasurableSpace α] [LinearOrderedRing R] [FloorRing R] [TopologicalSpace R]
[OrderTopology R] [MeasurableSpace R]
+#print Int.measurable_floor /-
theorem Int.measurable_floor [OpensMeasurableSpace R] : Measurable (Int.floor : R → ℤ) :=
measurable_to_countable fun x => by
simpa only [Int.preimage_floor_singleton] using measurableSet_Ico
#align int.measurable_floor Int.measurable_floor
+-/
+#print Measurable.floor /-
@[measurability]
theorem Measurable.floor [OpensMeasurableSpace R] {f : α → R} (hf : Measurable f) :
Measurable fun x => ⌊f x⌋ :=
Int.measurable_floor.comp hf
#align measurable.floor Measurable.floor
+-/
+#print Int.measurable_ceil /-
theorem Int.measurable_ceil [OpensMeasurableSpace R] : Measurable (Int.ceil : R → ℤ) :=
measurable_to_countable fun x => by
simpa only [Int.preimage_ceil_singleton] using measurableSet_Ioc
#align int.measurable_ceil Int.measurable_ceil
+-/
+#print Measurable.ceil /-
@[measurability]
theorem Measurable.ceil [OpensMeasurableSpace R] {f : α → R} (hf : Measurable f) :
Measurable fun x => ⌈f x⌉ :=
Int.measurable_ceil.comp hf
#align measurable.ceil Measurable.ceil
+-/
+#print measurable_fract /-
theorem measurable_fract [BorelSpace R] : Measurable (Int.fract : R → R) :=
by
intro s hs
rw [Int.preimage_fract]
exact MeasurableSet.iUnion fun z => measurable_id.sub_const _ (hs.inter measurableSet_Ico)
#align measurable_fract measurable_fract
+-/
+#print Measurable.fract /-
@[measurability]
theorem Measurable.fract [BorelSpace R] {f : α → R} (hf : Measurable f) :
Measurable fun x => Int.fract (f x) :=
measurable_fract.comp hf
#align measurable.fract Measurable.fract
+-/
+#print MeasurableSet.image_fract /-
theorem MeasurableSet.image_fract [BorelSpace R] {s : Set R} (hs : MeasurableSet s) :
MeasurableSet (Int.fract '' s) :=
by
simp only [Int.image_fract, sub_eq_add_neg, image_add_right']
exact MeasurableSet.iUnion fun m => (measurable_add_const _ hs).inter measurableSet_Ico
#align measurable_set.image_fract MeasurableSet.image_fract
+-/
end FloorRing
@@ -74,21 +88,37 @@ section FloorSemiring
variable {α R : Type _} [MeasurableSpace α] [LinearOrderedSemiring R] [FloorSemiring R]
[TopologicalSpace R] [OrderTopology R] [MeasurableSpace R] [OpensMeasurableSpace R] {f : α → R}
+#print Nat.measurable_floor /-
theorem Nat.measurable_floor : Measurable (Nat.floor : R → ℕ) :=
measurable_to_countable fun n => by
cases eq_or_ne ⌊n⌋₊ 0 <;> simp [*, Nat.preimage_floor_of_ne_zero]
#align nat.measurable_floor Nat.measurable_floor
+-/
+/- warning: measurable.nat_floor -> Measurable.nat_floor is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {R : Type.{u2}} [_inst_1 : MeasurableSpace.{u1} α] [_inst_2 : LinearOrderedSemiring.{u2} R] [_inst_3 : FloorSemiring.{u2} R (StrictOrderedSemiring.toOrderedSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R _inst_2))] [_inst_4 : TopologicalSpace.{u2} R] [_inst_5 : OrderTopology.{u2} R _inst_4 (PartialOrder.toPreorder.{u2} R (OrderedCancelAddCommMonoid.toPartialOrder.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R _inst_2))))] [_inst_6 : MeasurableSpace.{u2} R] [_inst_7 : OpensMeasurableSpace.{u2} R _inst_4 _inst_6] {f : α -> R}, (Measurable.{u1, u2} α R _inst_1 _inst_6 f) -> (Measurable.{u1, 0} α Nat _inst_1 Nat.instMeasurableSpace (fun (x : α) => Nat.floor.{u2} R (StrictOrderedSemiring.toOrderedSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R _inst_2)) _inst_3 (f x)))
+but is expected to have type
+ forall {α : Type.{u2}} {R : Type.{u1}} [_inst_1 : MeasurableSpace.{u2} α] [_inst_2 : LinearOrderedSemiring.{u1} R] [_inst_3 : FloorSemiring.{u1} R (StrictOrderedSemiring.toOrderedSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R _inst_2))] [_inst_4 : TopologicalSpace.{u1} R] [_inst_5 : OrderTopology.{u1} R _inst_4 (PartialOrder.toPreorder.{u1} R (StrictOrderedSemiring.toPartialOrder.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R _inst_2)))] [_inst_6 : MeasurableSpace.{u1} R] [_inst_7 : OpensMeasurableSpace.{u1} R _inst_4 _inst_6] {f : α -> R}, (Measurable.{u2, u1} α R _inst_1 _inst_6 f) -> (Measurable.{u2, 0} α Nat _inst_1 Nat.instMeasurableSpace (fun (x : α) => Nat.floor.{u1} R (StrictOrderedSemiring.toOrderedSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R _inst_2)) _inst_3 (f x)))
+Case conversion may be inaccurate. Consider using '#align measurable.nat_floor Measurable.nat_floorₓ'. -/
@[measurability]
theorem Measurable.nat_floor (hf : Measurable f) : Measurable fun x => ⌊f x⌋₊ :=
Nat.measurable_floor.comp hf
#align measurable.nat_floor Measurable.nat_floor
+#print Nat.measurable_ceil /-
theorem Nat.measurable_ceil : Measurable (Nat.ceil : R → ℕ) :=
measurable_to_countable fun n => by
cases eq_or_ne ⌈n⌉₊ 0 <;> simp [*, Nat.preimage_ceil_of_ne_zero]
#align nat.measurable_ceil Nat.measurable_ceil
+-/
+/- warning: measurable.nat_ceil -> Measurable.nat_ceil is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {R : Type.{u2}} [_inst_1 : MeasurableSpace.{u1} α] [_inst_2 : LinearOrderedSemiring.{u2} R] [_inst_3 : FloorSemiring.{u2} R (StrictOrderedSemiring.toOrderedSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R _inst_2))] [_inst_4 : TopologicalSpace.{u2} R] [_inst_5 : OrderTopology.{u2} R _inst_4 (PartialOrder.toPreorder.{u2} R (OrderedCancelAddCommMonoid.toPartialOrder.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R _inst_2))))] [_inst_6 : MeasurableSpace.{u2} R] [_inst_7 : OpensMeasurableSpace.{u2} R _inst_4 _inst_6] {f : α -> R}, (Measurable.{u1, u2} α R _inst_1 _inst_6 f) -> (Measurable.{u1, 0} α Nat _inst_1 Nat.instMeasurableSpace (fun (x : α) => Nat.ceil.{u2} R (StrictOrderedSemiring.toOrderedSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R _inst_2)) _inst_3 (f x)))
+but is expected to have type
+ forall {α : Type.{u2}} {R : Type.{u1}} [_inst_1 : MeasurableSpace.{u2} α] [_inst_2 : LinearOrderedSemiring.{u1} R] [_inst_3 : FloorSemiring.{u1} R (StrictOrderedSemiring.toOrderedSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R _inst_2))] [_inst_4 : TopologicalSpace.{u1} R] [_inst_5 : OrderTopology.{u1} R _inst_4 (PartialOrder.toPreorder.{u1} R (StrictOrderedSemiring.toPartialOrder.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R _inst_2)))] [_inst_6 : MeasurableSpace.{u1} R] [_inst_7 : OpensMeasurableSpace.{u1} R _inst_4 _inst_6] {f : α -> R}, (Measurable.{u2, u1} α R _inst_1 _inst_6 f) -> (Measurable.{u2, 0} α Nat _inst_1 Nat.instMeasurableSpace (fun (x : α) => Nat.ceil.{u1} R (StrictOrderedSemiring.toOrderedSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R _inst_2)) _inst_3 (f x)))
+Case conversion may be inaccurate. Consider using '#align measurable.nat_ceil Measurable.nat_ceilₓ'. -/
@[measurability]
theorem Measurable.nat_ceil (hf : Measurable f) : Measurable fun x => ⌈f x⌉₊ :=
Nat.measurable_ceil.comp hf
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -4,11 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
! This file was ported from Lean 3 source module measure_theory.function.floor
-! leanprover-community/mathlib commit d003c55042c3cd08aefd1ae9a42ef89441cdaaf3
+! leanprover-community/mathlib commit bf6a01357ff5684b1ebcd0f1a13be314fc82c0bf
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
-import Mathbin.MeasureTheory.Constructions.BorelSpace
+import Mathbin.MeasureTheory.Constructions.BorelSpace.Basic
/-!
# Measurability of `⌊x⌋` etc
mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee
@@ -51,7 +51,7 @@ theorem measurable_fract [BorelSpace R] : Measurable (Int.fract : R → R) :=
by
intro s hs
rw [Int.preimage_fract]
- exact MeasurableSet.unionᵢ fun z => measurable_id.sub_const _ (hs.inter measurableSet_Ico)
+ exact MeasurableSet.iUnion fun z => measurable_id.sub_const _ (hs.inter measurableSet_Ico)
#align measurable_fract measurable_fract
@[measurability]
@@ -64,7 +64,7 @@ theorem MeasurableSet.image_fract [BorelSpace R] {s : Set R} (hs : MeasurableSet
MeasurableSet (Int.fract '' s) :=
by
simp only [Int.image_fract, sub_eq_add_neg, image_add_right']
- exact MeasurableSet.unionᵢ fun m => (measurable_add_const _ hs).inter measurableSet_Ico
+ exact MeasurableSet.iUnion fun m => (measurable_add_const _ hs).inter measurableSet_Ico
#align measurable_set.image_fract MeasurableSet.image_fract
end FloorRing
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
cases'
(#9171)
I literally went through and regex'd some uses of cases'
, replacing them with rcases
; this is meant to be a low effort PR as I hope that tools can do this in the future.
rcases
is an easier replacement than cases
, though with better tools we could in future do a second pass converting simple rcases
added here (and existing ones) to cases
.
@@ -71,7 +71,7 @@ variable {α R : Type*} [MeasurableSpace α] [LinearOrderedSemiring R] [FloorSem
theorem Nat.measurable_floor : Measurable (Nat.floor : R → ℕ) :=
measurable_to_countable fun n => by
- cases' eq_or_ne ⌊n⌋₊ 0 with h h <;> simp_all [h, Nat.preimage_floor_of_ne_zero, -floor_eq_zero]
+ rcases eq_or_ne ⌊n⌋₊ 0 with h | h <;> simp [h, Nat.preimage_floor_of_ne_zero, -floor_eq_zero]
#align nat.measurable_floor Nat.measurable_floor
@[measurability]
@@ -81,7 +81,7 @@ theorem Measurable.nat_floor (hf : Measurable f) : Measurable fun x => ⌊f x⌋
theorem Nat.measurable_ceil : Measurable (Nat.ceil : R → ℕ) :=
measurable_to_countable fun n => by
- cases' eq_or_ne ⌈n⌉₊ 0 with h h <;> simp_all [h, Nat.preimage_ceil_of_ne_zero, -ceil_eq_zero]
+ rcases eq_or_ne ⌈n⌉₊ 0 with h | h <;> simp_all [h, Nat.preimage_ceil_of_ne_zero, -ceil_eq_zero]
#align nat.measurable_ceil Nat.measurable_ceil
@[measurability]
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -19,7 +19,7 @@ open Set
section FloorRing
-variable {α R : Type _} [MeasurableSpace α] [LinearOrderedRing R] [FloorRing R] [TopologicalSpace R]
+variable {α R : Type*} [MeasurableSpace α] [LinearOrderedRing R] [FloorRing R] [TopologicalSpace R]
[OrderTopology R] [MeasurableSpace R]
theorem Int.measurable_floor [OpensMeasurableSpace R] : Measurable (Int.floor : R → ℤ) :=
@@ -66,7 +66,7 @@ end FloorRing
section FloorSemiring
-variable {α R : Type _} [MeasurableSpace α] [LinearOrderedSemiring R] [FloorSemiring R]
+variable {α R : Type*} [MeasurableSpace α] [LinearOrderedSemiring R] [FloorSemiring R]
[TopologicalSpace R] [OrderTopology R] [MeasurableSpace R] [OpensMeasurableSpace R] {f : α → R}
theorem Nat.measurable_floor : Measurable (Nat.floor : R → ℕ) :=
@@ -2,14 +2,11 @@
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-
-! This file was ported from Lean 3 source module measure_theory.function.floor
-! leanprover-community/mathlib commit bf6a01357ff5684b1ebcd0f1a13be314fc82c0bf
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
+#align_import measure_theory.function.floor from "leanprover-community/mathlib"@"bf6a01357ff5684b1ebcd0f1a13be314fc82c0bf"
+
/-!
# Measurability of `⌊x⌋` etc
Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>
@@ -74,7 +74,7 @@ variable {α R : Type _} [MeasurableSpace α] [LinearOrderedSemiring R] [FloorSe
theorem Nat.measurable_floor : Measurable (Nat.floor : R → ℕ) :=
measurable_to_countable fun n => by
- cases' eq_or_ne ⌊n⌋₊ 0 with h h <;> simp_all [h, Nat.preimage_floor_of_ne_zero]
+ cases' eq_or_ne ⌊n⌋₊ 0 with h h <;> simp_all [h, Nat.preimage_floor_of_ne_zero, -floor_eq_zero]
#align nat.measurable_floor Nat.measurable_floor
@[measurability]
@@ -84,7 +84,7 @@ theorem Measurable.nat_floor (hf : Measurable f) : Measurable fun x => ⌊f x⌋
theorem Nat.measurable_ceil : Measurable (Nat.ceil : R → ℕ) :=
measurable_to_countable fun n => by
- cases' eq_or_ne ⌈n⌉₊ 0 with h h <;> simp_all [h, Nat.preimage_ceil_of_ne_zero]
+ cases' eq_or_ne ⌈n⌉₊ 0 with h h <;> simp_all [h, Nat.preimage_ceil_of_ne_zero, -ceil_eq_zero]
#align nat.measurable_ceil Nat.measurable_ceil
@[measurability]
The unported dependencies are
algebra.order.module
init.core
algebra.order.monoid.cancel.defs
algebra.abs
algebra.group_power.lemmas
init.data.list.basic
init.data.list.default
algebra.order.monoid.cancel.basic
topology.subset_properties
init.logic
The following 1 dependencies have changed in mathlib3 since they were ported, which may complicate porting this file