probability.process.adaptedMathlib.Probability.Process.Adapted

This file has been ported!

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

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Changes in mathlib3port

mathlib3
mathlib3port
Diff
@@ -3,8 +3,8 @@ Copyright (c) 2021 Kexing Ying. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying, Rémy Degenne
 -/
-import Mathbin.Probability.Process.Filtration
-import Mathbin.Topology.Instances.Discrete
+import Probability.Process.Filtration
+import Topology.Instances.Discrete
 
 #align_import probability.process.adapted from "leanprover-community/mathlib"@"e160cefedc932ce41c7049bf0c4b0f061d06216e"
 
Diff
@@ -2,15 +2,12 @@
 Copyright (c) 2021 Kexing Ying. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying, Rémy Degenne
-
-! This file was ported from Lean 3 source module probability.process.adapted
-! leanprover-community/mathlib commit e160cefedc932ce41c7049bf0c4b0f061d06216e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Probability.Process.Filtration
 import Mathbin.Topology.Instances.Discrete
 
+#align_import probability.process.adapted from "leanprover-community/mathlib"@"e160cefedc932ce41c7049bf0c4b0f061d06216e"
+
 /-!
 # Adapted and progressively measurable processes
 
Diff
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying, Rémy Degenne
 
 ! This file was ported from Lean 3 source module probability.process.adapted
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit e160cefedc932ce41c7049bf0c4b0f061d06216e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Topology.Instances.Discrete
 /-!
 # Adapted and progressively measurable processes
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines some standard definition from the theory of stochastic processes including
 filtrations and stopping times. These definitions are used to model the amount of information
 at a specific time and are the first step in formalizing stochastic processes.
Diff
@@ -207,7 +207,7 @@ protected theorem finset_prod' {γ} [CommMonoid β] [ContinuousMul β] {U : γ 
 protected theorem finset_prod {γ} [CommMonoid β] [ContinuousMul β] {U : γ → ι → Ω → β}
     {s : Finset γ} (h : ∀ c ∈ s, ProgMeasurable f (U c)) :
     ProgMeasurable f fun i a => ∏ c in s, U c i a := by convert prog_measurable.finset_prod' h;
-  ext (i a); simp only [Finset.prod_apply]
+  ext i a; simp only [Finset.prod_apply]
 #align measure_theory.prog_measurable.finset_prod MeasureTheory.ProgMeasurable.finset_prod
 #align measure_theory.prog_measurable.finset_sum MeasureTheory.ProgMeasurable.finset_sum
 -/
Diff
@@ -47,60 +47,79 @@ namespace MeasureTheory
 variable {Ω β ι : Type _} {m : MeasurableSpace Ω} [TopologicalSpace β] [Preorder ι]
   {u v : ι → Ω → β} {f : Filtration ι m}
 
+#print MeasureTheory.Adapted /-
 /-- A sequence of functions `u` is adapted to a filtration `f` if for all `i`,
 `u i` is `f i`-measurable. -/
 def Adapted (f : Filtration ι m) (u : ι → Ω → β) : Prop :=
   ∀ i : ι, strongly_measurable[f i] (u i)
 #align measure_theory.adapted MeasureTheory.Adapted
+-/
 
 namespace Adapted
 
+#print MeasureTheory.Adapted.mul /-
 @[protected, to_additive]
 theorem mul [Mul β] [ContinuousMul β] (hu : Adapted f u) (hv : Adapted f v) : Adapted f (u * v) :=
   fun i => (hu i).mul (hv i)
 #align measure_theory.adapted.mul MeasureTheory.Adapted.mul
 #align measure_theory.adapted.add MeasureTheory.Adapted.add
+-/
 
+#print MeasureTheory.Adapted.div /-
 @[protected, to_additive]
 theorem div [Div β] [ContinuousDiv β] (hu : Adapted f u) (hv : Adapted f v) : Adapted f (u / v) :=
   fun i => (hu i).div (hv i)
 #align measure_theory.adapted.div MeasureTheory.Adapted.div
 #align measure_theory.adapted.sub MeasureTheory.Adapted.sub
+-/
 
+#print MeasureTheory.Adapted.inv /-
 @[protected, to_additive]
 theorem inv [Group β] [TopologicalGroup β] (hu : Adapted f u) : Adapted f u⁻¹ := fun i => (hu i).inv
 #align measure_theory.adapted.inv MeasureTheory.Adapted.inv
 #align measure_theory.adapted.neg MeasureTheory.Adapted.neg
+-/
 
+#print MeasureTheory.Adapted.smul /-
 @[protected]
 theorem smul [SMul ℝ β] [ContinuousSMul ℝ β] (c : ℝ) (hu : Adapted f u) : Adapted f (c • u) :=
   fun i => (hu i).const_smul c
 #align measure_theory.adapted.smul MeasureTheory.Adapted.smul
+-/
 
+#print MeasureTheory.Adapted.stronglyMeasurable /-
 @[protected]
 theorem stronglyMeasurable {i : ι} (hf : Adapted f u) : strongly_measurable[m] (u i) :=
   (hf i).mono (f.le i)
 #align measure_theory.adapted.strongly_measurable MeasureTheory.Adapted.stronglyMeasurable
+-/
 
+#print MeasureTheory.Adapted.stronglyMeasurable_le /-
 theorem stronglyMeasurable_le {i j : ι} (hf : Adapted f u) (hij : i ≤ j) :
     strongly_measurable[f j] (u i) :=
   (hf i).mono (f.mono hij)
 #align measure_theory.adapted.strongly_measurable_le MeasureTheory.Adapted.stronglyMeasurable_le
+-/
 
 end Adapted
 
+#print MeasureTheory.adapted_const /-
 theorem adapted_const (f : Filtration ι m) (x : β) : Adapted f fun _ _ => x := fun i =>
   stronglyMeasurable_const
 #align measure_theory.adapted_const MeasureTheory.adapted_const
+-/
 
 variable (β)
 
+#print MeasureTheory.adapted_zero /-
 theorem adapted_zero [Zero β] (f : Filtration ι m) : Adapted f (0 : ι → Ω → β) := fun i =>
   @stronglyMeasurable_zero Ω β (f i) _ _
 #align measure_theory.adapted_zero MeasureTheory.adapted_zero
+-/
 
 variable {β}
 
+#print MeasureTheory.Filtration.adapted_natural /-
 theorem Filtration.adapted_natural [MetrizableSpace β] [mβ : MeasurableSpace β] [BorelSpace β]
     {u : ι → Ω → β} (hum : ∀ i, strongly_measurable[m] (u i)) :
     Adapted (Filtration.natural u hum) u := by
@@ -109,7 +128,9 @@ theorem Filtration.adapted_natural [MetrizableSpace β] [mβ : MeasurableSpace 
   rw [stronglyMeasurable_iff_measurable_separable]
   exact ⟨measurable_iff_comap_le.2 le_rfl, (hum i).isSeparable_range⟩
 #align measure_theory.filtration.adapted_natural MeasureTheory.Filtration.adapted_natural
+-/
 
+#print MeasureTheory.ProgMeasurable /-
 /-- Progressively measurable process. A sequence of functions `u` is said to be progressively
 measurable with respect to a filtration `f` if at each point in time `i`, `u` restricted to
 `set.Iic i × Ω` is measurable with respect to the product `measurable_space` structure where the
@@ -120,16 +141,20 @@ def ProgMeasurable [MeasurableSpace ι] (f : Filtration ι m) (u : ι → Ω →
   ∀ i,
     strongly_measurable[Subtype.instMeasurableSpace.Prod (f i)] fun p : Set.Iic i × Ω => u p.1 p.2
 #align measure_theory.prog_measurable MeasureTheory.ProgMeasurable
+-/
 
+#print MeasureTheory.progMeasurable_const /-
 theorem progMeasurable_const [MeasurableSpace ι] (f : Filtration ι m) (b : β) :
     ProgMeasurable f (fun _ _ => b : ι → Ω → β) := fun i =>
   @stronglyMeasurable_const _ _ (Subtype.instMeasurableSpace.Prod (f i)) _ _
 #align measure_theory.prog_measurable_const MeasureTheory.progMeasurable_const
+-/
 
 namespace ProgMeasurable
 
 variable [MeasurableSpace ι]
 
+#print MeasureTheory.ProgMeasurable.adapted /-
 protected theorem adapted (h : ProgMeasurable f u) : Adapted f u :=
   by
   intro i
@@ -138,7 +163,9 @@ protected theorem adapted (h : ProgMeasurable f u) : Adapted f u :=
   rw [this]
   exact (h i).comp_measurable measurable_prod_mk_left
 #align measure_theory.prog_measurable.adapted MeasureTheory.ProgMeasurable.adapted
+-/
 
+#print MeasureTheory.ProgMeasurable.comp /-
 protected theorem comp {t : ι → Ω → ι} [TopologicalSpace ι] [BorelSpace ι] [MetrizableSpace ι]
     (h : ProgMeasurable f u) (ht : ProgMeasurable f t) (ht_le : ∀ i ω, t i ω ≤ i) :
     ProgMeasurable f fun i ω => u (t i ω) ω :=
@@ -152,16 +179,20 @@ protected theorem comp {t : ι → Ω → ι} [TopologicalSpace ι] [BorelSpace
   rw [this]
   exact (h i).comp_measurable ((ht i).Measurable.subtype_mk.prod_mk measurable_snd)
 #align measure_theory.prog_measurable.comp MeasureTheory.ProgMeasurable.comp
+-/
 
 section Arithmetic
 
+#print MeasureTheory.ProgMeasurable.mul /-
 @[to_additive]
 protected theorem mul [Mul β] [ContinuousMul β] (hu : ProgMeasurable f u)
     (hv : ProgMeasurable f v) : ProgMeasurable f fun i ω => u i ω * v i ω := fun i =>
   (hu i).mul (hv i)
 #align measure_theory.prog_measurable.mul MeasureTheory.ProgMeasurable.mul
 #align measure_theory.prog_measurable.add MeasureTheory.ProgMeasurable.add
+-/
 
+#print MeasureTheory.ProgMeasurable.finset_prod' /-
 @[to_additive]
 protected theorem finset_prod' {γ} [CommMonoid β] [ContinuousMul β] {U : γ → ι → Ω → β}
     {s : Finset γ} (h : ∀ c ∈ s, ProgMeasurable f (U c)) : ProgMeasurable f (∏ c in s, U c) :=
@@ -169,7 +200,9 @@ protected theorem finset_prod' {γ} [CommMonoid β] [ContinuousMul β] {U : γ 
     (progMeasurable_const _ 1) h
 #align measure_theory.prog_measurable.finset_prod' MeasureTheory.ProgMeasurable.finset_prod'
 #align measure_theory.prog_measurable.finset_sum' MeasureTheory.ProgMeasurable.finset_sum'
+-/
 
+#print MeasureTheory.ProgMeasurable.finset_prod /-
 @[to_additive]
 protected theorem finset_prod {γ} [CommMonoid β] [ContinuousMul β] {U : γ → ι → Ω → β}
     {s : Finset γ} (h : ∀ c ∈ s, ProgMeasurable f (U c)) :
@@ -177,24 +210,30 @@ protected theorem finset_prod {γ} [CommMonoid β] [ContinuousMul β] {U : γ 
   ext (i a); simp only [Finset.prod_apply]
 #align measure_theory.prog_measurable.finset_prod MeasureTheory.ProgMeasurable.finset_prod
 #align measure_theory.prog_measurable.finset_sum MeasureTheory.ProgMeasurable.finset_sum
+-/
 
+#print MeasureTheory.ProgMeasurable.inv /-
 @[to_additive]
 protected theorem inv [Group β] [TopologicalGroup β] (hu : ProgMeasurable f u) :
     ProgMeasurable f fun i ω => (u i ω)⁻¹ := fun i => (hu i).inv
 #align measure_theory.prog_measurable.inv MeasureTheory.ProgMeasurable.inv
 #align measure_theory.prog_measurable.neg MeasureTheory.ProgMeasurable.neg
+-/
 
+#print MeasureTheory.ProgMeasurable.div /-
 @[to_additive]
 protected theorem div [Group β] [TopologicalGroup β] (hu : ProgMeasurable f u)
     (hv : ProgMeasurable f v) : ProgMeasurable f fun i ω => u i ω / v i ω := fun i =>
   (hu i).div (hv i)
 #align measure_theory.prog_measurable.div MeasureTheory.ProgMeasurable.div
 #align measure_theory.prog_measurable.sub MeasureTheory.ProgMeasurable.sub
+-/
 
 end Arithmetic
 
 end ProgMeasurable
 
+#print MeasureTheory.progMeasurable_of_tendsto' /-
 theorem progMeasurable_of_tendsto' {γ} [MeasurableSpace ι] [PseudoMetrizableSpace β]
     (fltr : Filter γ) [fltr.ne_bot] [fltr.IsCountablyGenerated] {U : γ → ι → Ω → β}
     (h : ∀ l, ProgMeasurable f (U l)) (h_tendsto : Tendsto U fltr (𝓝 u)) : ProgMeasurable f u :=
@@ -209,12 +248,16 @@ theorem progMeasurable_of_tendsto' {γ} [MeasurableSpace ι] [PseudoMetrizableSp
   rw [tendsto_nhds] at h_tendsto ⊢
   exact fun s hs h_mem => h_tendsto {g | g x.snd ∈ s} (hs.Preimage (continuous_apply x.snd)) h_mem
 #align measure_theory.prog_measurable_of_tendsto' MeasureTheory.progMeasurable_of_tendsto'
+-/
 
+#print MeasureTheory.progMeasurable_of_tendsto /-
 theorem progMeasurable_of_tendsto [MeasurableSpace ι] [PseudoMetrizableSpace β] {U : ℕ → ι → Ω → β}
     (h : ∀ l, ProgMeasurable f (U l)) (h_tendsto : Tendsto U atTop (𝓝 u)) : ProgMeasurable f u :=
   progMeasurable_of_tendsto' atTop h h_tendsto
 #align measure_theory.prog_measurable_of_tendsto MeasureTheory.progMeasurable_of_tendsto
+-/
 
+#print MeasureTheory.Adapted.progMeasurable_of_continuous /-
 /-- A continuous and adapted process is progressively measurable. -/
 theorem Adapted.progMeasurable_of_continuous [TopologicalSpace ι] [MetrizableSpace ι]
     [SecondCountableTopology ι] [MeasurableSpace ι] [OpensMeasurableSpace ι]
@@ -223,7 +266,9 @@ theorem Adapted.progMeasurable_of_continuous [TopologicalSpace ι] [MetrizableSp
   @stronglyMeasurable_uncurry_of_continuous_of_stronglyMeasurable _ _ (Set.Iic i) _ _ _ _ _ _ _
     (f i) _ (fun ω => (hu_cont ω).comp continuous_induced_dom) fun j => (h j).mono (f.mono j.Prop)
 #align measure_theory.adapted.prog_measurable_of_continuous MeasureTheory.Adapted.progMeasurable_of_continuous
+-/
 
+#print MeasureTheory.Adapted.progMeasurable_of_discrete /-
 /-- For filtrations indexed by a discrete order, `adapted` and `prog_measurable` are equivalent.
 This lemma provides `adapted f u → prog_measurable f u`.
 See `prog_measurable.adapted` for the reverse direction, which is true more generally. -/
@@ -232,7 +277,9 @@ theorem Adapted.progMeasurable_of_discrete [TopologicalSpace ι] [DiscreteTopolo
     [PseudoMetrizableSpace β] (h : Adapted f u) : ProgMeasurable f u :=
   h.progMeasurable_of_continuous fun _ => continuous_of_discreteTopology
 #align measure_theory.adapted.prog_measurable_of_discrete MeasureTheory.Adapted.progMeasurable_of_discrete
+-/
 
+#print MeasureTheory.Predictable.adapted /-
 -- this dot notation will make more sense once we have a more general definition for predictable
 theorem Predictable.adapted {f : Filtration ℕ m} {u : ℕ → Ω → β} (hu : Adapted f fun n => u (n + 1))
     (hu0 : strongly_measurable[f 0] (u 0)) : Adapted f u := fun n =>
@@ -240,6 +287,7 @@ theorem Predictable.adapted {f : Filtration ℕ m} {u : ℕ → Ω → β} (hu :
   | 0 => hu0
   | n + 1 => (hu n).mono (f.mono n.le_succ)
 #align measure_theory.predictable.adapted MeasureTheory.Predictable.adapted
+-/
 
 end MeasureTheory
 
Diff
@@ -207,7 +207,7 @@ theorem progMeasurable_of_tendsto' {γ} [MeasurableSpace ι] [PseudoMetrizableSp
   intro x
   specialize h_tendsto x.fst
   rw [tendsto_nhds] at h_tendsto ⊢
-  exact fun s hs h_mem => h_tendsto { g | g x.snd ∈ s } (hs.Preimage (continuous_apply x.snd)) h_mem
+  exact fun s hs h_mem => h_tendsto {g | g x.snd ∈ s} (hs.Preimage (continuous_apply x.snd)) h_mem
 #align measure_theory.prog_measurable_of_tendsto' MeasureTheory.progMeasurable_of_tendsto'
 
 theorem progMeasurable_of_tendsto [MeasurableSpace ι] [PseudoMetrizableSpace β] {U : ℕ → ι → Ω → β}
Diff
@@ -203,10 +203,10 @@ theorem progMeasurable_of_tendsto' {γ} [MeasurableSpace ι] [PseudoMetrizableSp
   apply
     @stronglyMeasurable_of_tendsto (Set.Iic i × Ω) β γ (MeasurableSpace.prod _ (f i)) _ _ fltr _ _ _
       _ fun l => h l i
-  rw [tendsto_pi_nhds] at h_tendsto⊢
+  rw [tendsto_pi_nhds] at h_tendsto ⊢
   intro x
   specialize h_tendsto x.fst
-  rw [tendsto_nhds] at h_tendsto⊢
+  rw [tendsto_nhds] at h_tendsto ⊢
   exact fun s hs h_mem => h_tendsto { g | g x.snd ∈ s } (hs.Preimage (continuous_apply x.snd)) h_mem
 #align measure_theory.prog_measurable_of_tendsto' MeasureTheory.progMeasurable_of_tendsto'
 
Diff
@@ -40,7 +40,7 @@ adapted, progressively measurable
 
 open Filter Order TopologicalSpace
 
-open Classical MeasureTheory NNReal ENNReal Topology BigOperators
+open scoped Classical MeasureTheory NNReal ENNReal Topology BigOperators
 
 namespace MeasureTheory
 
Diff
@@ -173,11 +173,8 @@ protected theorem finset_prod' {γ} [CommMonoid β] [ContinuousMul β] {U : γ 
 @[to_additive]
 protected theorem finset_prod {γ} [CommMonoid β] [ContinuousMul β] {U : γ → ι → Ω → β}
     {s : Finset γ} (h : ∀ c ∈ s, ProgMeasurable f (U c)) :
-    ProgMeasurable f fun i a => ∏ c in s, U c i a :=
-  by
-  convert prog_measurable.finset_prod' h
-  ext (i a)
-  simp only [Finset.prod_apply]
+    ProgMeasurable f fun i a => ∏ c in s, U c i a := by convert prog_measurable.finset_prod' h;
+  ext (i a); simp only [Finset.prod_apply]
 #align measure_theory.prog_measurable.finset_prod MeasureTheory.ProgMeasurable.finset_prod
 #align measure_theory.prog_measurable.finset_sum MeasureTheory.ProgMeasurable.finset_sum
 
Diff
@@ -105,7 +105,7 @@ theorem Filtration.adapted_natural [MetrizableSpace β] [mβ : MeasurableSpace 
     {u : ι → Ω → β} (hum : ∀ i, strongly_measurable[m] (u i)) :
     Adapted (Filtration.natural u hum) u := by
   intro i
-  refine' strongly_measurable.mono _ (le_supᵢ₂_of_le i (le_refl i) le_rfl)
+  refine' strongly_measurable.mono _ (le_iSup₂_of_le i (le_refl i) le_rfl)
   rw [stronglyMeasurable_iff_measurable_separable]
   exact ⟨measurable_iff_comap_le.2 le_rfl, (hum i).isSeparable_range⟩
 #align measure_theory.filtration.adapted_natural MeasureTheory.Filtration.adapted_natural
Diff
@@ -117,12 +117,13 @@ measurable with respect to a filtration `f` if at each point in time `i`, `u` re
 The usual definition uses the interval `[0,i]`, which we replace by `set.Iic i`. We recover the
 usual definition for index types `ℝ≥0` or `ℕ`. -/
 def ProgMeasurable [MeasurableSpace ι] (f : Filtration ι m) (u : ι → Ω → β) : Prop :=
-  ∀ i, strongly_measurable[Subtype.measurableSpace.Prod (f i)] fun p : Set.Iic i × Ω => u p.1 p.2
+  ∀ i,
+    strongly_measurable[Subtype.instMeasurableSpace.Prod (f i)] fun p : Set.Iic i × Ω => u p.1 p.2
 #align measure_theory.prog_measurable MeasureTheory.ProgMeasurable
 
 theorem progMeasurable_const [MeasurableSpace ι] (f : Filtration ι m) (b : β) :
     ProgMeasurable f (fun _ _ => b : ι → Ω → β) := fun i =>
-  @stronglyMeasurable_const _ _ (Subtype.measurableSpace.Prod (f i)) _ _
+  @stronglyMeasurable_const _ _ (Subtype.instMeasurableSpace.Prod (f i)) _ _
 #align measure_theory.prog_measurable_const MeasureTheory.progMeasurable_const
 
 namespace ProgMeasurable
Diff
@@ -135,7 +135,7 @@ protected theorem adapted (h : ProgMeasurable f u) : Adapted f u :=
   have : u i = (fun p : Set.Iic i × Ω => u p.1 p.2) ∘ fun x => (⟨i, set.mem_Iic.mpr le_rfl⟩, x) :=
     rfl
   rw [this]
-  exact (h i).compMeasurable measurable_prod_mk_left
+  exact (h i).comp_measurable measurable_prod_mk_left
 #align measure_theory.prog_measurable.adapted MeasureTheory.ProgMeasurable.adapted
 
 protected theorem comp {t : ι → Ω → ι} [TopologicalSpace ι] [BorelSpace ι] [MetrizableSpace ι]
@@ -149,7 +149,7 @@ protected theorem comp {t : ι → Ω → ι} [TopologicalSpace ι] [BorelSpace
         (⟨t (p.fst : ι) p.snd, set.mem_Iic.mpr ((ht_le _ _).trans p.fst.prop)⟩, p.snd) :=
     rfl
   rw [this]
-  exact (h i).compMeasurable ((ht i).Measurable.subtype_mk.prod_mk measurable_snd)
+  exact (h i).comp_measurable ((ht i).Measurable.subtype_mk.prod_mk measurable_snd)
 #align measure_theory.prog_measurable.comp MeasureTheory.ProgMeasurable.comp
 
 section Arithmetic
Diff
@@ -40,7 +40,7 @@ adapted, progressively measurable
 
 open Filter Order TopologicalSpace
 
-open Classical MeasureTheory NNReal Ennreal Topology BigOperators
+open Classical MeasureTheory NNReal ENNReal Topology BigOperators
 
 namespace MeasureTheory
 
Diff
@@ -62,8 +62,8 @@ theorem mul [Mul β] [ContinuousMul β] (hu : Adapted f u) (hv : Adapted f v) :
 #align measure_theory.adapted.add MeasureTheory.Adapted.add
 
 @[protected, to_additive]
-theorem div [Div β] [HasContinuousDiv β] (hu : Adapted f u) (hv : Adapted f v) :
-    Adapted f (u / v) := fun i => (hu i).div (hv i)
+theorem div [Div β] [ContinuousDiv β] (hu : Adapted f u) (hv : Adapted f v) : Adapted f (u / v) :=
+  fun i => (hu i).div (hv i)
 #align measure_theory.adapted.div MeasureTheory.Adapted.div
 #align measure_theory.adapted.sub MeasureTheory.Adapted.sub
 

Changes in mathlib4

mathlib3
mathlib4
chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

Diff
@@ -41,7 +41,7 @@ open scoped Classical MeasureTheory NNReal ENNReal Topology BigOperators
 
 namespace MeasureTheory
 
-variable {Ω β ι : Type _} {m : MeasurableSpace Ω} [TopologicalSpace β] [Preorder ι]
+variable {Ω β ι : Type*} {m : MeasurableSpace Ω} [TopologicalSpace β] [Preorder ι]
   {u v : ι → Ω → β} {f : Filtration ι m}
 
 /-- A sequence of functions `u` is adapted to a filtration `f` if for all `i`,
chore: script to replace headers with #align_import statements (#5979)

Open in Gitpod

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

Diff
@@ -2,15 +2,12 @@
 Copyright (c) 2021 Kexing Ying. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying, Rémy Degenne
-
-! This file was ported from Lean 3 source module probability.process.adapted
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Probability.Process.Filtration
 import Mathlib.Topology.Instances.Discrete
 
+#align_import probability.process.adapted from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Adapted and progressively measurable processes
 
feat: port Probability.Process.Adapted (#5205)

Dependencies 12 + 1001

1002 files ported (98.8%)
457112 lines ported (98.8%)
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The unported dependencies are

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