probability.process.adapted
⟷
Mathlib.Probability.Process.Adapted
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
@@ -3,8 +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"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -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
mathlib commit https://github.com/leanprover-community/mathlib/commit/0723536a0522d24fc2f159a096fb3304bef77472
@@ -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.
mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
@@ -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
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
@@ -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
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -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}
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -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'
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -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
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -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
mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee
@@ -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
mathlib commit https://github.com/leanprover-community/mathlib/commit/d4437c68c8d350fc9d4e95e1e174409db35e30d7
@@ -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
mathlib commit https://github.com/leanprover-community/mathlib/commit/92c69b77c5a7dc0f7eeddb552508633305157caa
@@ -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
mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee
@@ -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
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -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
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -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`,
@@ -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
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