probability.martingale.optional_sampling ⟷ Mathlib.Probability.Martingale.OptionalSampling

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -38,11 +38,13 @@ open scoped MeasureTheory BigOperators ENNReal
 
 open TopologicalSpace
 
+/- warning: discrete_topology.second_countable_topology_of_countable clashes with discrete_topology.second_countable_topology_of_encodable -> DiscreteTopology.secondCountableTopology_of_countable
+Case conversion may be inaccurate. Consider using '#align discrete_topology.second_countable_topology_of_countable DiscreteTopology.secondCountableTopology_of_countableₓ'. -/
 #print DiscreteTopology.secondCountableTopology_of_countable /-
 -- TODO after the port: move to topology/instances/discrete
 instance (priority := 100) DiscreteTopology.secondCountableTopology_of_countable {α : Type _}
     [TopologicalSpace α] [DiscreteTopology α] [Countable α] : SecondCountableTopology α :=
-  @DiscreteTopology.secondCountableTopology_of_encodable _ _ _ (Encodable.ofCountable _)
+  @DiscreteTopology.secondCountableTopology_of_countable _ _ _ (Encodable.ofCountable _)
 #align discrete_topology.second_countable_topology_of_countable DiscreteTopology.secondCountableTopology_of_countable
 -/
 
@@ -103,7 +105,7 @@ theorem stoppedValue_ae_eq_restrict_eq (h : Martingale f ℱ μ) (hτ : IsStoppi
       (condexp_stopping_time_ae_eq_restrict_eq_const_of_le_const h hτ hτ_le i).symm
   rw [Filter.EventuallyEq, ae_restrict_iff' (ℱ.le _ _ (hτ.measurable_set_eq i))]
   refine' Filter.eventually_of_forall fun x hx => _
-  rw [Set.mem_setOf_eq] at hx 
+  rw [Set.mem_setOf_eq] at hx
   simp_rw [stopped_value, hx]
 #align measure_theory.martingale.stopped_value_ae_eq_restrict_eq MeasureTheory.Martingale.stoppedValue_ae_eq_restrict_eq
 -/
@@ -221,7 +223,7 @@ theorem condexp_stoppedValue_stopping_time_ae_eq_restrict_le (h : Martingale f 
         (hτ.measurable_set_le_stopping_time hσ) _ _ _
     · intro t ht
       rw [Set.inter_comm _ t] at ht ⊢
-      rw [hτ.measurable_set_inter_le_iff, is_stopping_time.measurable_set_min_iff hτ hσ] at ht 
+      rw [hτ.measurable_set_inter_le_iff, is_stopping_time.measurable_set_min_iff hτ hσ] at ht
       exact ht.2
     · refine' strongly_measurable.indicator _ (hτ.measurable_set_le_stopping_time hσ)
       refine' Measurable.stronglyMeasurable _
@@ -251,10 +253,10 @@ theorem stoppedValue_min_ae_eq_condexp [SigmaFiniteFiltration μ ℱ] (h : Marti
         μ[stopped_value f τ|hσ.measurable_space]
       by
       rw [ae_restrict_iff' (hσ.measurable_space_le _ (hσ.measurable_set_le_stopping_time hτ).compl)]
-      rw [Filter.EventuallyEq, ae_restrict_iff'] at this 
+      rw [Filter.EventuallyEq, ae_restrict_iff'] at this
       swap; · exact hτ.measurable_space_le _ (hτ.measurable_set_le_stopping_time hσ)
       filter_upwards [this] with x hx hx_mem
-      simp only [Set.mem_compl_iff, Set.mem_setOf_eq, not_le] at hx_mem 
+      simp only [Set.mem_compl_iff, Set.mem_setOf_eq, not_le] at hx_mem
       exact hx hx_mem.le
     refine'
       Filter.EventuallyEq.trans _ ((condexp_min_stopping_time_ae_eq_restrict_le hτ hσ).trans _)

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,8 +3,8 @@ Copyright (c) 2023 Rémy Degenne. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
 -/
-import Mathbin.Order.SuccPred.LinearLocallyFinite
-import Mathbin.Probability.Martingale.Basic
+import Order.SuccPred.LinearLocallyFinite
+import Probability.Martingale.Basic
 
 #align_import probability.martingale.optional_sampling from "leanprover-community/mathlib"@"f2ad3645af9effcdb587637dc28a6074edc813f9"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,15 +2,12 @@
 Copyright (c) 2023 Rémy Degenne. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
-
-! This file was ported from Lean 3 source module probability.martingale.optional_sampling
-! leanprover-community/mathlib commit f2ad3645af9effcdb587637dc28a6074edc813f9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Order.SuccPred.LinearLocallyFinite
 import Mathbin.Probability.Martingale.Basic
 
+#align_import probability.martingale.optional_sampling from "leanprover-community/mathlib"@"f2ad3645af9effcdb587637dc28a6074edc813f9"
+
 /-!
 # Optional sampling theorem
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/f2ad3645af9effcdb587637dc28a6074edc813f9

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
 
 ! This file was ported from Lean 3 source module probability.martingale.optional_sampling
-! leanprover-community/mathlib commit ba074af83b6cf54c3104e59402b39410ddbd6dca
+! leanprover-community/mathlib commit f2ad3645af9effcdb587637dc28a6074edc813f9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Probability.Martingale.Basic
 /-!
 # Optional sampling theorem
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 If `τ` is a bounded stopping time and `σ` is another stopping time, then the value of a martingale
 `f` at the stopping time `min τ σ` is almost everywhere equal to
 `μ[stopped_value f τ | hσ.measurable_space]`.

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -38,11 +38,13 @@ open scoped MeasureTheory BigOperators ENNReal
 
 open TopologicalSpace
 
+#print DiscreteTopology.secondCountableTopology_of_countable /-
 -- TODO after the port: move to topology/instances/discrete
 instance (priority := 100) DiscreteTopology.secondCountableTopology_of_countable {α : Type _}
     [TopologicalSpace α] [DiscreteTopology α] [Countable α] : SecondCountableTopology α :=
   @DiscreteTopology.secondCountableTopology_of_encodable _ _ _ (Encodable.ofCountable _)
 #align discrete_topology.second_countable_topology_of_countable DiscreteTopology.secondCountableTopology_of_countable
+-/
 
 namespace MeasureTheory
 
@@ -57,6 +59,7 @@ variable {ι : Type _} [LinearOrder ι] [TopologicalSpace ι] [OrderTopology ι]
   [FirstCountableTopology ι] {ℱ : Filtration ι m} [SigmaFiniteFiltration μ ℱ] {τ σ : Ω → ι}
   {f : ι → Ω → E} {i n : ι}
 
+#print MeasureTheory.Martingale.condexp_stopping_time_ae_eq_restrict_eq_const /-
 theorem condexp_stopping_time_ae_eq_restrict_eq_const
     [(Filter.atTop : Filter ι).IsCountablyGenerated] (h : Martingale f ℱ μ)
     (hτ : IsStoppingTime ℱ τ) [SigmaFinite (μ.trim hτ.measurableSpace_le)] (hin : i ≤ n) :
@@ -68,7 +71,9 @@ theorem condexp_stopping_time_ae_eq_restrict_eq_const
       (hτ.measurable_set_eq' i) fun t => _
   rw [Set.inter_comm _ t, is_stopping_time.measurable_set_inter_eq_iff]
 #align measure_theory.martingale.condexp_stopping_time_ae_eq_restrict_eq_const MeasureTheory.Martingale.condexp_stopping_time_ae_eq_restrict_eq_const
+-/
 
+#print MeasureTheory.Martingale.condexp_stopping_time_ae_eq_restrict_eq_const_of_le_const /-
 theorem condexp_stopping_time_ae_eq_restrict_eq_const_of_le_const (h : Martingale f ℱ μ)
     (hτ : IsStoppingTime ℱ τ) (hτ_le : ∀ x, τ x ≤ n)
     [SigmaFinite (μ.trim (hτ.measurableSpace_le_of_le hτ_le))] (i : ι) :
@@ -86,7 +91,9 @@ theorem condexp_stopping_time_ae_eq_restrict_eq_const_of_le_const (h : Martingal
     rintro rfl
     exact hin (hτ_le x)
 #align measure_theory.martingale.condexp_stopping_time_ae_eq_restrict_eq_const_of_le_const MeasureTheory.Martingale.condexp_stopping_time_ae_eq_restrict_eq_const_of_le_const
+-/
 
+#print MeasureTheory.Martingale.stoppedValue_ae_eq_restrict_eq /-
 theorem stoppedValue_ae_eq_restrict_eq (h : Martingale f ℱ μ) (hτ : IsStoppingTime ℱ τ)
     (hτ_le : ∀ x, τ x ≤ n) [SigmaFinite (μ.trim (hτ.measurableSpace_le_of_le hτ_le))] (i : ι) :
     stoppedValue f τ =ᵐ[μ.restrict {x | τ x = i}] μ[f n|hτ.MeasurableSpace] :=
@@ -99,7 +106,9 @@ theorem stoppedValue_ae_eq_restrict_eq (h : Martingale f ℱ μ) (hτ : IsStoppi
   rw [Set.mem_setOf_eq] at hx 
   simp_rw [stopped_value, hx]
 #align measure_theory.martingale.stopped_value_ae_eq_restrict_eq MeasureTheory.Martingale.stoppedValue_ae_eq_restrict_eq
+-/
 
+#print MeasureTheory.Martingale.stoppedValue_ae_eq_condexp_of_le_const_of_countable_range /-
 /-- The value of a martingale `f` at a stopping time `τ` bounded by `n` is the conditional
 expectation of `f n` with respect to the σ-algebra generated by `τ`. -/
 theorem stoppedValue_ae_eq_condexp_of_le_const_of_countable_range (h : Martingale f ℱ μ)
@@ -116,7 +125,9 @@ theorem stoppedValue_ae_eq_condexp_of_le_const_of_countable_range (h : Martingal
   rw [this, ae_eq_restrict_bUnion_iff _ h_countable_range]
   exact fun i hi => stopped_value_ae_eq_restrict_eq h _ hτ_le i
 #align measure_theory.martingale.stopped_value_ae_eq_condexp_of_le_const_of_countable_range MeasureTheory.Martingale.stoppedValue_ae_eq_condexp_of_le_const_of_countable_range
+-/
 
+#print MeasureTheory.Martingale.stoppedValue_ae_eq_condexp_of_le_const /-
 /-- The value of a martingale `f` at a stopping time `τ` bounded by `n` is the conditional
 expectation of `f n` with respect to the σ-algebra generated by `τ`. -/
 theorem stoppedValue_ae_eq_condexp_of_le_const [Countable ι] (h : Martingale f ℱ μ)
@@ -125,7 +136,9 @@ theorem stoppedValue_ae_eq_condexp_of_le_const [Countable ι] (h : Martingale f
     stoppedValue f τ =ᵐ[μ] μ[f n|hτ.MeasurableSpace] :=
   h.stoppedValue_ae_eq_condexp_of_le_const_of_countable_range hτ hτ_le (Set.to_countable _)
 #align measure_theory.martingale.stopped_value_ae_eq_condexp_of_le_const MeasureTheory.Martingale.stoppedValue_ae_eq_condexp_of_le_const
+-/
 
+#print MeasureTheory.Martingale.stoppedValue_ae_eq_condexp_of_le_of_countable_range /-
 /-- If `τ` and `σ` are two stopping times with `σ ≤ τ` and `τ` is bounded, then the value of a
 martingale `f` at `σ` is the conditional expectation of its value at `τ` with respect to the
 σ-algebra generated by `σ`. -/
@@ -152,7 +165,9 @@ theorem stoppedValue_ae_eq_condexp_of_le_of_countable_range (h : Martingale f 
         (fun x => (hσ_le_τ x).trans (hτ_le x)) hσ_countable_range
   · exact hσ.measurable_space_mono hτ hσ_le_τ
 #align measure_theory.martingale.stopped_value_ae_eq_condexp_of_le_of_countable_range MeasureTheory.Martingale.stoppedValue_ae_eq_condexp_of_le_of_countable_range
+-/
 
+#print MeasureTheory.Martingale.stoppedValue_ae_eq_condexp_of_le /-
 /-- If `τ` and `σ` are two stopping times with `σ ≤ τ` and `τ` is bounded, then the value of a
 martingale `f` at `σ` is the conditional expectation of its value at `τ` with respect to the
 σ-algebra generated by `σ`. -/
@@ -163,6 +178,7 @@ theorem stoppedValue_ae_eq_condexp_of_le [Countable ι] (h : Martingale f ℱ μ
   h.stoppedValue_ae_eq_condexp_of_le_of_countable_range hτ hσ hσ_le_τ hτ_le (Set.to_countable _)
     (Set.to_countable _)
 #align measure_theory.martingale.stopped_value_ae_eq_condexp_of_le MeasureTheory.Martingale.stoppedValue_ae_eq_condexp_of_le
+-/
 
 end FirstCountableTopology
 
@@ -178,6 +194,7 @@ variable {ι : Type _} [LinearOrder ι] [LocallyFiniteOrder ι] [OrderBot ι] [T
   [DiscreteTopology ι] [MeasurableSpace ι] [BorelSpace ι] [MeasurableSpace E] [BorelSpace E]
   [SecondCountableTopology E] {ℱ : Filtration ι m} {τ σ : Ω → ι} {f : ι → Ω → E} {i n : ι}
 
+#print MeasureTheory.Martingale.condexp_stoppedValue_stopping_time_ae_eq_restrict_le /-
 theorem condexp_stoppedValue_stopping_time_ae_eq_restrict_le (h : Martingale f ℱ μ)
     (hτ : IsStoppingTime ℱ τ) (hσ : IsStoppingTime ℱ σ) [SigmaFinite (μ.trim hσ.measurableSpace_le)]
     (hτ_le : ∀ x, τ x ≤ n) :
@@ -213,7 +230,9 @@ theorem condexp_stoppedValue_stopping_time_ae_eq_restrict_le (h : Martingale f 
       simp only [hx, Set.indicator_of_not_mem, not_false_iff]
   exact condexp_of_ae_strongly_measurable' hσ.measurable_space_le h_meas h_int
 #align measure_theory.martingale.condexp_stopped_value_stopping_time_ae_eq_restrict_le MeasureTheory.Martingale.condexp_stoppedValue_stopping_time_ae_eq_restrict_le
+-/
 
+#print MeasureTheory.Martingale.stoppedValue_min_ae_eq_condexp /-
 /-- **Optional Sampling theorem**. If `τ` is a bounded stopping time and `σ` is another stopping
 time, then the value of a martingale `f` at the stopping time `min τ σ` is almost everywhere equal
 to the conditional expectation of `f` stopped at `τ` with respect to the σ-algebra generated
@@ -250,6 +269,7 @@ theorem stoppedValue_min_ae_eq_condexp [SigmaFiniteFiltration μ ℱ] (h : Marti
       rw [h1]
       exact (condexp_stopped_value_stopping_time_ae_eq_restrict_le h hτ hσ hτ_le).symm
 #align measure_theory.martingale.stopped_value_min_ae_eq_condexp MeasureTheory.Martingale.stoppedValue_min_ae_eq_condexp
+-/
 
 end SubsetOfNat
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

Implement a porting note to move this instance to a much more natural file.

@@ -35,12 +35,6 @@ open scoped MeasureTheory BigOperators ENNReal
 
 open TopologicalSpace
 
--- Porting note: move to `Topology/Instances/Discrete`
-instance (priority := 100) DiscreteTopology.secondCountableTopology_of_countable {α : Type*}
-    [TopologicalSpace α] [DiscreteTopology α] [Countable α] : SecondCountableTopology α :=
-  @DiscreteTopology.secondCountableTopology_of_encodable _ _ _ (Encodable.ofCountable _)
-#align discrete_topology.second_countable_topology_of_countable DiscreteTopology.secondCountableTopology_of_countable
-
 namespace MeasureTheory
 
 namespace Martingale

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

This has nice performance benefits.

@@ -36,7 +36,7 @@ open scoped MeasureTheory BigOperators ENNReal
 open TopologicalSpace
 
 -- Porting note: move to `Topology/Instances/Discrete`
-instance (priority := 100) DiscreteTopology.secondCountableTopology_of_countable {α : Type _}
+instance (priority := 100) DiscreteTopology.secondCountableTopology_of_countable {α : Type*}
     [TopologicalSpace α] [DiscreteTopology α] [Countable α] : SecondCountableTopology α :=
   @DiscreteTopology.secondCountableTopology_of_encodable _ _ _ (Encodable.ofCountable _)
 #align discrete_topology.second_countable_topology_of_countable DiscreteTopology.secondCountableTopology_of_countable
@@ -45,12 +45,12 @@ namespace MeasureTheory
 
 namespace Martingale
 
-variable {Ω E : Type _} {m : MeasurableSpace Ω} {μ : Measure Ω} [NormedAddCommGroup E]
+variable {Ω E : Type*} {m : MeasurableSpace Ω} {μ : Measure Ω} [NormedAddCommGroup E]
   [NormedSpace ℝ E] [CompleteSpace E]
 
 section FirstCountableTopology
 
-variable {ι : Type _} [LinearOrder ι] [TopologicalSpace ι] [OrderTopology ι]
+variable {ι : Type*} [LinearOrder ι] [TopologicalSpace ι] [OrderTopology ι]
   [FirstCountableTopology ι] {ℱ : Filtration ι m} [SigmaFiniteFiltration μ ℱ] {τ σ : Ω → ι}
   {f : ι → Ω → E} {i n : ι}
 
@@ -156,7 +156,7 @@ a subset of `ℕ`. `ι` is equipped with the discrete topology, which is also th
 and is a measurable space with the Borel σ-algebra. -/
 
 
-variable {ι : Type _} [LinearOrder ι] [LocallyFiniteOrder ι] [OrderBot ι] [TopologicalSpace ι]
+variable {ι : Type*} [LinearOrder ι] [LocallyFiniteOrder ι] [OrderBot ι] [TopologicalSpace ι]
   [DiscreteTopology ι] [MeasurableSpace ι] [BorelSpace ι] [MeasurableSpace E] [BorelSpace E]
   [SecondCountableTopology E] {ℱ : Filtration ι m} {τ σ : Ω → ι} {f : ι → Ω → E} {i n : ι}
 

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2023 Rémy Degenne. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
-
-! This file was ported from Lean 3 source module probability.martingale.optional_sampling
-! leanprover-community/mathlib commit ba074af83b6cf54c3104e59402b39410ddbd6dca
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Order.SuccPred.LinearLocallyFinite
 import Mathlib.Probability.Martingale.Basic
 
+#align_import probability.martingale.optional_sampling from "leanprover-community/mathlib"@"ba074af83b6cf54c3104e59402b39410ddbd6dca"
+
 /-!
 # Optional sampling theorem
 

@@ -38,7 +38,7 @@ open scoped MeasureTheory BigOperators ENNReal
 
 open TopologicalSpace
 
--- TODO after the port: move to `Topology/Instances/Discrete`
+-- Porting note: move to `Topology/Instances/Discrete`
 instance (priority := 100) DiscreteTopology.secondCountableTopology_of_countable {α : Type _}
     [TopologicalSpace α] [DiscreteTopology α] [Countable α] : SecondCountableTopology α :=
   @DiscreteTopology.secondCountableTopology_of_encodable _ _ _ (Encodable.ofCountable _)