probability.martingale.optional_stopping

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.

Changes in mathlib3

70fd9563

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

e8e130de

bump to nightly-2024-04-09-08

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

659ec6f7

Diff

@@ -244,7 +244,7 @@ theorem maximal_ineq [IsFiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnon
       rw [Set.mem_setOf_eq] at hω
       have : hitting f {y : ℝ | ↑ε ≤ y} 0 n ω = n :=
         by
-        simp only [hitting, Set.mem_setOf_eq, exists_prop, Pi.coe_nat, Nat.cast_id,
+        simp only [hitting, Set.mem_setOf_eq, exists_prop, Pi.natCast_def, Nat.cast_id,
           ite_eq_right_iff, forall_exists_index, and_imp]
         intro m hm hεm
         exact

e8e130de

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -91,7 +91,7 @@ theorem submartingale_of_expected_stoppedValue_mono [IsFiniteMeasure μ] (hadp :
       ⟨j, fun x => le_rfl⟩
   rwa [stopped_value_const, stopped_value_piecewise_const,
     integral_piecewise (𝒢.le _ _ hs) (hint _).IntegrableOn (hint _).IntegrableOn, ←
-    integral_add_compl (𝒢.le _ _ hs) (hint j), add_le_add_iff_right] at hf 
+    integral_add_compl (𝒢.le _ _ hs) (hint j), add_le_add_iff_right] at hf
 #align measure_theory.submartingale_of_expected_stopped_value_mono MeasureTheory.submartingale_of_expected_stoppedValue_mono
 -/
 
@@ -150,7 +150,7 @@ theorem smul_le_stoppedValue_hitting [IsFiniteMeasure μ] (hsub : Submartingale
         (ε : ℝ) ≤ stopped_value f (hitting f {y : ℝ | ↑ε ≤ y} 0 n) ω :=
     by
     intro x hx
-    simp_rw [le_sup'_iff, mem_range, Nat.lt_succ_iff] at hx 
+    simp_rw [le_sup'_iff, mem_range, Nat.lt_succ_iff] at hx
     refine' stopped_value_hitting_mem _
     simp only [Set.mem_setOf_eq, exists_prop, hn]
     exact
@@ -216,7 +216,7 @@ theorem maximal_ineq [IsFiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnon
             measurable_const
       exacts [(hsub.integrable _).IntegrableOn, (hsub.integrable _).IntegrableOn,
         integral_nonneg (hnonneg _), integral_nonneg (hnonneg _)]
-    rwa [hadd, ENNReal.add_le_add_iff_right ENNReal.ofReal_ne_top] at this 
+    rwa [hadd, ENNReal.add_le_add_iff_right ENNReal.ofReal_ne_top] at this
   calc
     ε • μ {ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω} +
           ENNReal.ofReal
@@ -241,7 +241,7 @@ theorem maximal_ineq [IsFiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnon
                 measurable_const)
               _))
       intro ω hω
-      rw [Set.mem_setOf_eq] at hω 
+      rw [Set.mem_setOf_eq] at hω
       have : hitting f {y : ℝ | ↑ε ≤ y} 0 n ω = n :=
         by
         simp only [hitting, Set.mem_setOf_eq, exists_prop, Pi.coe_nat, Nat.cast_id,

e8e130de

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -85,6 +85,13 @@ theorem submartingale_of_expected_stoppedValue_mono [IsFiniteMeasure μ] (hadp :
   by
   refine' submartingale_of_set_integral_le hadp hint fun i j hij s hs => _
   classical
+  specialize
+    hf (s.piecewise (fun _ => i) fun _ => j) _ (is_stopping_time_piecewise_const hij hs)
+      (is_stopping_time_const 𝒢 j) (fun x => (ite_le_sup _ _ _).trans (max_eq_right hij).le)
+      ⟨j, fun x => le_rfl⟩
+  rwa [stopped_value_const, stopped_value_piecewise_const,
+    integral_piecewise (𝒢.le _ _ hs) (hint _).IntegrableOn (hint _).IntegrableOn, ←
+    integral_add_compl (𝒢.le _ _ hs) (hint j), add_le_add_iff_right] at hf 
 #align measure_theory.submartingale_of_expected_stopped_value_mono MeasureTheory.submartingale_of_expected_stoppedValue_mono
 -/

e8e130de

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -85,13 +85,6 @@ theorem submartingale_of_expected_stoppedValue_mono [IsFiniteMeasure μ] (hadp :
   by
   refine' submartingale_of_set_integral_le hadp hint fun i j hij s hs => _
   classical
-  specialize
-    hf (s.piecewise (fun _ => i) fun _ => j) _ (is_stopping_time_piecewise_const hij hs)
-      (is_stopping_time_const 𝒢 j) (fun x => (ite_le_sup _ _ _).trans (max_eq_right hij).le)
-      ⟨j, fun x => le_rfl⟩
-  rwa [stopped_value_const, stopped_value_piecewise_const,
-    integral_piecewise (𝒢.le _ _ hs) (hint _).IntegrableOn (hint _).IntegrableOn, ←
-    integral_add_compl (𝒢.le _ _ hs) (hint j), add_le_add_iff_right] at hf 
 #align measure_theory.submartingale_of_expected_stopped_value_mono MeasureTheory.submartingale_of_expected_stoppedValue_mono
 -/

e8e130de

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2022 Kexing Ying. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
 -/
-import Mathbin.Probability.Process.HittingTime
-import Mathbin.Probability.Martingale.Basic
+import Probability.Process.HittingTime
+import Probability.Martingale.Basic
 
 #align_import probability.martingale.optional_stopping from "leanprover-community/mathlib"@"e8e130de9dba4ed6897183c3193c752ffadbcc77"

e8e130de

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Kexing Ying. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
-
-! This file was ported from Lean 3 source module probability.martingale.optional_stopping
-! leanprover-community/mathlib commit e8e130de9dba4ed6897183c3193c752ffadbcc77
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Probability.Process.HittingTime
 import Mathbin.Probability.Martingale.Basic
 
+#align_import probability.martingale.optional_stopping from "leanprover-community/mathlib"@"e8e130de9dba4ed6897183c3193c752ffadbcc77"
+
 /-! # Optional stopping theorem (fair game theorem)
 
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.

e8e130de

bump to nightly-2023-06-22-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/6285167a053ad0990fc88e56c48ccd9fae6550eb

2424c6fa

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
 
 ! This file was ported from Lean 3 source module probability.martingale.optional_stopping
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit e8e130de9dba4ed6897183c3193c752ffadbcc77
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Probability.Martingale.Basic
 
 /-! # Optional stopping theorem (fair game theorem)
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The optional stopping theorem states that an adapted integrable process `f` is a submartingale if
 and only if for all bounded stopping times `τ` and `π` such that `τ ≤ π`, the
 stopped value of `f` at `τ` has expectation smaller than its stopped value at `π`.

70fd9563

bump to nightly-2023-06-20-05

mathlib commit https://github.com/leanprover-community/mathlib/commit/0723536a0522d24fc2f159a096fb3304bef77472

4ff05811

Diff

@@ -37,6 +37,7 @@ namespace MeasureTheory
 variable {Ω : Type _} {m0 : MeasurableSpace Ω} {μ : Measure Ω} {𝒢 : Filtration ℕ m0} {f : ℕ → Ω → ℝ}
   {τ π : Ω → ℕ}
 
+#print MeasureTheory.Submartingale.expected_stoppedValue_mono /-
 -- We may generalize the below lemma to functions taking value in a `normed_lattice_add_comm_group`.
 -- Similarly, generalize `(super/)submartingale.set_integral_le`.
 /-- Given a submartingale `f` and bounded stopping times `τ` and `π` such that `τ ≤ π`, the
@@ -67,7 +68,9 @@ theorem Submartingale.expected_stoppedValue_mono [SigmaFiniteFiltration μ 𝒢]
   · exact hf.integrable_stopped_value hπ hbdd
   · exact hf.integrable_stopped_value hτ fun ω => le_trans (hle ω) (hbdd ω)
 #align measure_theory.submartingale.expected_stopped_value_mono MeasureTheory.Submartingale.expected_stoppedValue_mono
+-/
 
+#print MeasureTheory.submartingale_of_expected_stoppedValue_mono /-
 /-- The converse direction of the optional stopping theorem, i.e. an adapted integrable process `f`
 is a submartingale if for all bounded stopping times `τ` and `π` such that `τ ≤ π`, the
 stopped value of `f` at `τ` has expectation smaller than its stopped value at `π`. -/
@@ -90,7 +93,9 @@ theorem submartingale_of_expected_stoppedValue_mono [IsFiniteMeasure μ] (hadp :
     integral_piecewise (𝒢.le _ _ hs) (hint _).IntegrableOn (hint _).IntegrableOn, ←
     integral_add_compl (𝒢.le _ _ hs) (hint j), add_le_add_iff_right] at hf 
 #align measure_theory.submartingale_of_expected_stopped_value_mono MeasureTheory.submartingale_of_expected_stoppedValue_mono
+-/
 
+#print MeasureTheory.submartingale_iff_expected_stoppedValue_mono /-
 /-- **The optional stopping theorem** (fair game theorem): an adapted integrable process `f`
 is a submartingale if and only if for all bounded stopping times `τ` and `π` such that `τ ≤ π`, the
 stopped value of `f` at `τ` has expectation smaller than its stopped value at `π`. -/
@@ -104,7 +109,9 @@ theorem submartingale_iff_expected_stoppedValue_mono [IsFiniteMeasure μ] (hadp
   ⟨fun hf _ _ hτ hπ hle ⟨N, hN⟩ => hf.expected_stoppedValue_mono hτ hπ hle hN,
     submartingale_of_expected_stoppedValue_mono hadp hint⟩
 #align measure_theory.submartingale_iff_expected_stopped_value_mono MeasureTheory.submartingale_iff_expected_stoppedValue_mono
+-/
 
+#print MeasureTheory.Submartingale.stoppedProcess /-
 /-- The stopped process of a submartingale with respect to a stopping time is a submartingale. -/
 @[protected]
 theorem Submartingale.stoppedProcess [IsFiniteMeasure μ] (h : Submartingale f 𝒢 μ)
@@ -122,11 +129,13 @@ theorem Submartingale.stoppedProcess [IsFiniteMeasure μ] (h : Submartingale f 
     exact fun i =>
       h.integrable_stopped_value ((is_stopping_time_const _ i).min hτ) fun ω => min_le_left _ _
 #align measure_theory.submartingale.stopped_process MeasureTheory.Submartingale.stoppedProcess
+-/
 
 section Maximal
 
 open Finset
 
+#print MeasureTheory.smul_le_stoppedValue_hitting /-
 theorem smul_le_stoppedValue_hitting [IsFiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) {ε : ℝ≥0}
     (n : ℕ) :
     ε • μ {ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω} ≤
@@ -161,7 +170,9 @@ theorem smul_le_stoppedValue_hitting [IsFiniteMeasure μ] (hsub : Submartingale
   · exact ENNReal.mul_ne_top (by simp) (measure_ne_top _ _)
   · exact le_trans (mul_nonneg ε.coe_nonneg ENNReal.toReal_nonneg) h
 #align measure_theory.smul_le_stopped_value_hitting MeasureTheory.smul_le_stoppedValue_hitting
+-/
 
+#print MeasureTheory.maximal_ineq /-
 /-- **Doob's maximal inequality**: Given a non-negative submartingale `f`, for all `ε : ℝ≥0`,
 we have `ε • μ {ε ≤ f* n} ≤ ∫ ω in {ε ≤ f* n}, f n` where `f* n ω = max_{k ≤ n}, f k ω`.
 
@@ -276,6 +287,7 @@ theorem maximal_ineq [IsFiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnon
         hsub.expected_stopped_value_mono (hitting_is_stopping_time hsub.adapted measurableSet_Ici)
           (is_stopping_time_const _ _) (fun ω => hitting_le ω) (fun ω => le_rfl : ∀ ω, n ≤ n)
 #align measure_theory.maximal_ineq MeasureTheory.maximal_ineq
+-/
 
 end Maximal

70fd9563

bump to nightly-2023-06-09-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

16afdc39

Diff

@@ -275,7 +275,6 @@ theorem maximal_ineq [IsFiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnon
       exact
         hsub.expected_stopped_value_mono (hitting_is_stopping_time hsub.adapted measurableSet_Ici)
           (is_stopping_time_const _ _) (fun ω => hitting_le ω) (fun ω => le_rfl : ∀ ω, n ≤ n)
-    
 #align measure_theory.maximal_ineq MeasureTheory.maximal_ineq
 
 end Maximal

70fd9563

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -48,11 +48,11 @@ theorem Submartingale.expected_stoppedValue_mono [SigmaFiniteFiltration μ 𝒢]
   by
   rw [← sub_nonneg, ← integral_sub', stopped_value_sub_eq_sum' hle hbdd]
   · simp only [Finset.sum_apply]
-    have : ∀ i, measurable_set[𝒢 i] { ω : Ω | τ ω ≤ i ∧ i < π ω } :=
+    have : ∀ i, measurable_set[𝒢 i] {ω : Ω | τ ω ≤ i ∧ i < π ω} :=
       by
       intro i
       refine' (hτ i).inter _
-      convert(hπ i).compl
+      convert (hπ i).compl
       ext x
       simpa
     rw [integral_finset_sum]
@@ -71,7 +71,7 @@ theorem Submartingale.expected_stoppedValue_mono [SigmaFiniteFiltration μ 𝒢]
 /-- The converse direction of the optional stopping theorem, i.e. an adapted integrable process `f`
 is a submartingale if for all bounded stopping times `τ` and `π` such that `τ ≤ π`, the
 stopped value of `f` at `τ` has expectation smaller than its stopped value at `π`. -/
-theorem submartingale_of_expected_stoppedValue_mono [FiniteMeasure μ] (hadp : Adapted 𝒢 f)
+theorem submartingale_of_expected_stoppedValue_mono [IsFiniteMeasure μ] (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ)
     (hf :
       ∀ τ π : Ω → ℕ,
@@ -82,19 +82,19 @@ theorem submartingale_of_expected_stoppedValue_mono [FiniteMeasure μ] (hadp : A
   by
   refine' submartingale_of_set_integral_le hadp hint fun i j hij s hs => _
   classical
-    specialize
-      hf (s.piecewise (fun _ => i) fun _ => j) _ (is_stopping_time_piecewise_const hij hs)
-        (is_stopping_time_const 𝒢 j) (fun x => (ite_le_sup _ _ _).trans (max_eq_right hij).le)
-        ⟨j, fun x => le_rfl⟩
-    rwa [stopped_value_const, stopped_value_piecewise_const,
-      integral_piecewise (𝒢.le _ _ hs) (hint _).IntegrableOn (hint _).IntegrableOn, ←
-      integral_add_compl (𝒢.le _ _ hs) (hint j), add_le_add_iff_right] at hf 
+  specialize
+    hf (s.piecewise (fun _ => i) fun _ => j) _ (is_stopping_time_piecewise_const hij hs)
+      (is_stopping_time_const 𝒢 j) (fun x => (ite_le_sup _ _ _).trans (max_eq_right hij).le)
+      ⟨j, fun x => le_rfl⟩
+  rwa [stopped_value_const, stopped_value_piecewise_const,
+    integral_piecewise (𝒢.le _ _ hs) (hint _).IntegrableOn (hint _).IntegrableOn, ←
+    integral_add_compl (𝒢.le _ _ hs) (hint j), add_le_add_iff_right] at hf 
 #align measure_theory.submartingale_of_expected_stopped_value_mono MeasureTheory.submartingale_of_expected_stoppedValue_mono
 
 /-- **The optional stopping theorem** (fair game theorem): an adapted integrable process `f`
 is a submartingale if and only if for all bounded stopping times `τ` and `π` such that `τ ≤ π`, the
 stopped value of `f` at `τ` has expectation smaller than its stopped value at `π`. -/
-theorem submartingale_iff_expected_stoppedValue_mono [FiniteMeasure μ] (hadp : Adapted 𝒢 f)
+theorem submartingale_iff_expected_stoppedValue_mono [IsFiniteMeasure μ] (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ) :
     Submartingale f 𝒢 μ ↔
       ∀ τ π : Ω → ℕ,
@@ -107,7 +107,7 @@ theorem submartingale_iff_expected_stoppedValue_mono [FiniteMeasure μ] (hadp :
 
 /-- The stopped process of a submartingale with respect to a stopping time is a submartingale. -/
 @[protected]
-theorem Submartingale.stoppedProcess [FiniteMeasure μ] (h : Submartingale f 𝒢 μ)
+theorem Submartingale.stoppedProcess [IsFiniteMeasure μ] (h : Submartingale f 𝒢 μ)
     (hτ : IsStoppingTime 𝒢 τ) : Submartingale (stoppedProcess f τ) 𝒢 μ :=
   by
   rw [submartingale_iff_expected_stopped_value_mono]
@@ -127,18 +127,18 @@ section Maximal
 
 open Finset
 
-theorem smul_le_stoppedValue_hitting [FiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) {ε : ℝ≥0}
+theorem smul_le_stoppedValue_hitting [IsFiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) {ε : ℝ≥0}
     (n : ℕ) :
-    ε • μ { ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω } ≤
+    ε • μ {ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω} ≤
       ENNReal.ofReal
-        (∫ ω in { ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω },
-          stoppedValue f (hitting f { y : ℝ | ↑ε ≤ y } 0 n) ω ∂μ) :=
+        (∫ ω in {ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω},
+          stoppedValue f (hitting f {y : ℝ | ↑ε ≤ y} 0 n) ω ∂μ) :=
   by
-  have hn : Set.Icc 0 n = { k | k ≤ n } := by ext x; simp
+  have hn : Set.Icc 0 n = {k | k ≤ n} := by ext x; simp
   have :
     ∀ ω,
       ((ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω) →
-        (ε : ℝ) ≤ stopped_value f (hitting f { y : ℝ | ↑ε ≤ y } 0 n) ω :=
+        (ε : ℝ) ≤ stopped_value f (hitting f {y : ℝ | ↑ε ≤ y} 0 n) ω :=
     by
     intro x hx
     simp_rw [le_sup'_iff, mem_range, Nat.lt_succ_iff] at hx 
@@ -167,26 +167,25 @@ we have `ε • μ {ε ≤ f* n} ≤ ∫ ω in {ε ≤ f* n}, f n` where `f* n 
 
 In some literature, the Doob's maximal inequality refers to what we call Doob's Lp inequality
 (which is a corollary of this lemma and will be proved in an upcomming PR). -/
-theorem maximal_ineq [FiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnonneg : 0 ≤ f) {ε : ℝ≥0}
+theorem maximal_ineq [IsFiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnonneg : 0 ≤ f) {ε : ℝ≥0}
     (n : ℕ) :
-    ε • μ { ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω } ≤
+    ε • μ {ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω} ≤
       ENNReal.ofReal
-        (∫ ω in { ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω },
+        (∫ ω in {ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω},
           f n ω ∂μ) :=
   by
   suffices
-    ε • μ { ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω } +
+    ε • μ {ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω} +
         ENNReal.ofReal
-          (∫ ω in { ω | ((range (n + 1)).sup' nonempty_range_succ fun k => f k ω) < ε }, f n ω ∂μ) ≤
+          (∫ ω in {ω | ((range (n + 1)).sup' nonempty_range_succ fun k => f k ω) < ε}, f n ω ∂μ) ≤
       ENNReal.ofReal (μ[f n])
     by
     have hadd :
       ENNReal.ofReal (∫ ω, f n ω ∂μ) =
         ENNReal.ofReal
-            (∫ ω in { ω | ↑ε ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω },
-              f n ω ∂μ) +
+            (∫ ω in {ω | ↑ε ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω}, f n ω ∂μ) +
           ENNReal.ofReal
-            (∫ ω in { ω | ((range (n + 1)).sup' nonempty_range_succ fun k => f k ω) < ↑ε },
+            (∫ ω in {ω | ((range (n + 1)).sup' nonempty_range_succ fun k => f k ω) < ↑ε},
               f n ω ∂μ) :=
       by
       rw [← ENNReal.ofReal_add, ← integral_union]
@@ -208,16 +207,15 @@ theorem maximal_ineq [FiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnonne
         integral_nonneg (hnonneg _), integral_nonneg (hnonneg _)]
     rwa [hadd, ENNReal.add_le_add_iff_right ENNReal.ofReal_ne_top] at this 
   calc
-    ε • μ { ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω } +
+    ε • μ {ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω} +
           ENNReal.ofReal
-            (∫ ω in { ω | ((range (n + 1)).sup' nonempty_range_succ fun k => f k ω) < ε },
-              f n ω ∂μ) ≤
+            (∫ ω in {ω | ((range (n + 1)).sup' nonempty_range_succ fun k => f k ω) < ε}, f n ω ∂μ) ≤
         ENNReal.ofReal
-            (∫ ω in { ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω },
-              stopped_value f (hitting f { y : ℝ | ↑ε ≤ y } 0 n) ω ∂μ) +
+            (∫ ω in {ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω},
+              stopped_value f (hitting f {y : ℝ | ↑ε ≤ y} 0 n) ω ∂μ) +
           ENNReal.ofReal
-            (∫ ω in { ω | ((range (n + 1)).sup' nonempty_range_succ fun k => f k ω) < ε },
-              stopped_value f (hitting f { y : ℝ | ↑ε ≤ y } 0 n) ω ∂μ) :=
+            (∫ ω in {ω | ((range (n + 1)).sup' nonempty_range_succ fun k => f k ω) < ε},
+              stopped_value f (hitting f {y : ℝ | ↑ε ≤ y} 0 n) ω ∂μ) :=
       by
       refine'
         add_le_add (smul_le_stopped_value_hitting hsub _)
@@ -233,7 +231,7 @@ theorem maximal_ineq [FiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnonne
               _))
       intro ω hω
       rw [Set.mem_setOf_eq] at hω 
-      have : hitting f { y : ℝ | ↑ε ≤ y } 0 n ω = n :=
+      have : hitting f {y : ℝ | ↑ε ≤ y} 0 n ω = n :=
         by
         simp only [hitting, Set.mem_setOf_eq, exists_prop, Pi.coe_nat, Nat.cast_id,
           ite_eq_right_iff, forall_exists_index, and_imp]
@@ -242,7 +240,7 @@ theorem maximal_ineq [FiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnonne
           False.elim
             ((not_le.2 hω) ((le_sup'_iff _).2 ⟨m, mem_range.2 (Nat.lt_succ_of_le hm.2), hεm⟩))
       simp_rw [stopped_value, this]
-    _ = ENNReal.ofReal (∫ ω, stopped_value f (hitting f { y : ℝ | ↑ε ≤ y } 0 n) ω ∂μ) :=
+    _ = ENNReal.ofReal (∫ ω, stopped_value f (hitting f {y : ℝ | ↑ε ≤ y} 0 n) ω ∂μ) :=
       by
       rw [← ENNReal.ofReal_add, ← integral_union]
       · conv_rhs => rw [← integral_univ]

70fd9563

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -88,7 +88,7 @@ theorem submartingale_of_expected_stoppedValue_mono [FiniteMeasure μ] (hadp : A
         ⟨j, fun x => le_rfl⟩
     rwa [stopped_value_const, stopped_value_piecewise_const,
       integral_piecewise (𝒢.le _ _ hs) (hint _).IntegrableOn (hint _).IntegrableOn, ←
-      integral_add_compl (𝒢.le _ _ hs) (hint j), add_le_add_iff_right] at hf
+      integral_add_compl (𝒢.le _ _ hs) (hint j), add_le_add_iff_right] at hf 
 #align measure_theory.submartingale_of_expected_stopped_value_mono MeasureTheory.submartingale_of_expected_stoppedValue_mono
 
 /-- **The optional stopping theorem** (fair game theorem): an adapted integrable process `f`
@@ -141,7 +141,7 @@ theorem smul_le_stoppedValue_hitting [FiniteMeasure μ] (hsub : Submartingale f
         (ε : ℝ) ≤ stopped_value f (hitting f { y : ℝ | ↑ε ≤ y } 0 n) ω :=
     by
     intro x hx
-    simp_rw [le_sup'_iff, mem_range, Nat.lt_succ_iff] at hx
+    simp_rw [le_sup'_iff, mem_range, Nat.lt_succ_iff] at hx 
     refine' stopped_value_hitting_mem _
     simp only [Set.mem_setOf_eq, exists_prop, hn]
     exact
@@ -204,9 +204,9 @@ theorem maximal_ineq [FiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnonne
             (Finset.measurable_range_sup'' fun n _ =>
               (hsub.strongly_measurable n).Measurable.le (𝒢.le n))
             measurable_const
-      exacts[(hsub.integrable _).IntegrableOn, (hsub.integrable _).IntegrableOn,
+      exacts [(hsub.integrable _).IntegrableOn, (hsub.integrable _).IntegrableOn,
         integral_nonneg (hnonneg _), integral_nonneg (hnonneg _)]
-    rwa [hadd, ENNReal.add_le_add_iff_right ENNReal.ofReal_ne_top] at this
+    rwa [hadd, ENNReal.add_le_add_iff_right ENNReal.ofReal_ne_top] at this 
   calc
     ε • μ { ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω } +
           ENNReal.ofReal
@@ -232,7 +232,7 @@ theorem maximal_ineq [FiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnonne
                 measurable_const)
               _))
       intro ω hω
-      rw [Set.mem_setOf_eq] at hω
+      rw [Set.mem_setOf_eq] at hω 
       have : hitting f { y : ℝ | ↑ε ≤ y } 0 n ω = n :=
         by
         simp only [hitting, Set.mem_setOf_eq, exists_prop, Pi.coe_nat, Nat.cast_id,
@@ -269,7 +269,7 @@ theorem maximal_ineq [FiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnonne
           integrable.integrable_on
             (hsub.integrable_stopped_value (hitting_is_stopping_time hsub.adapted measurableSet_Ici)
               hitting_le)
-      exacts[integral_nonneg fun x => hnonneg _ _, integral_nonneg fun x => hnonneg _ _]
+      exacts [integral_nonneg fun x => hnonneg _ _, integral_nonneg fun x => hnonneg _ _]
     _ ≤ ENNReal.ofReal (μ[f n]) :=
       by
       refine' ENNReal.ofReal_le_ofReal _

70fd9563

bump to nightly-2023-05-28-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

8d353152

Diff

@@ -30,7 +30,7 @@ This file also contains Doob's maximal inequality: given a non-negative submarti
  -/
 
 
-open NNReal ENNReal MeasureTheory ProbabilityTheory
+open scoped NNReal ENNReal MeasureTheory ProbabilityTheory
 
 namespace MeasureTheory

70fd9563

bump to nightly-2023-05-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6797a637

Diff

@@ -134,9 +134,7 @@ theorem smul_le_stoppedValue_hitting [FiniteMeasure μ] (hsub : Submartingale f
         (∫ ω in { ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω },
           stoppedValue f (hitting f { y : ℝ | ↑ε ≤ y } 0 n) ω ∂μ) :=
   by
-  have hn : Set.Icc 0 n = { k | k ≤ n } := by
-    ext x
-    simp
+  have hn : Set.Icc 0 n = { k | k ≤ n } := by ext x; simp
   have :
     ∀ ω,
       ((ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω) →

70fd9563

bump to nightly-2023-05-09-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/d4437c68c8d350fc9d4e95e1e174409db35e30d7

244524af

Diff

@@ -71,7 +71,7 @@ theorem Submartingale.expected_stoppedValue_mono [SigmaFiniteFiltration μ 𝒢]
 /-- The converse direction of the optional stopping theorem, i.e. an adapted integrable process `f`
 is a submartingale if for all bounded stopping times `τ` and `π` such that `τ ≤ π`, the
 stopped value of `f` at `τ` has expectation smaller than its stopped value at `π`. -/
-theorem submartingale_of_expected_stoppedValue_mono [IsFiniteMeasure μ] (hadp : Adapted 𝒢 f)
+theorem submartingale_of_expected_stoppedValue_mono [FiniteMeasure μ] (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ)
     (hf :
       ∀ τ π : Ω → ℕ,
@@ -94,7 +94,7 @@ theorem submartingale_of_expected_stoppedValue_mono [IsFiniteMeasure μ] (hadp :
 /-- **The optional stopping theorem** (fair game theorem): an adapted integrable process `f`
 is a submartingale if and only if for all bounded stopping times `τ` and `π` such that `τ ≤ π`, the
 stopped value of `f` at `τ` has expectation smaller than its stopped value at `π`. -/
-theorem submartingale_iff_expected_stoppedValue_mono [IsFiniteMeasure μ] (hadp : Adapted 𝒢 f)
+theorem submartingale_iff_expected_stoppedValue_mono [FiniteMeasure μ] (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ) :
     Submartingale f 𝒢 μ ↔
       ∀ τ π : Ω → ℕ,
@@ -107,7 +107,7 @@ theorem submartingale_iff_expected_stoppedValue_mono [IsFiniteMeasure μ] (hadp
 
 /-- The stopped process of a submartingale with respect to a stopping time is a submartingale. -/
 @[protected]
-theorem Submartingale.stoppedProcess [IsFiniteMeasure μ] (h : Submartingale f 𝒢 μ)
+theorem Submartingale.stoppedProcess [FiniteMeasure μ] (h : Submartingale f 𝒢 μ)
     (hτ : IsStoppingTime 𝒢 τ) : Submartingale (stoppedProcess f τ) 𝒢 μ :=
   by
   rw [submartingale_iff_expected_stopped_value_mono]
@@ -127,7 +127,7 @@ section Maximal
 
 open Finset
 
-theorem smul_le_stoppedValue_hitting [IsFiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) {ε : ℝ≥0}
+theorem smul_le_stoppedValue_hitting [FiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) {ε : ℝ≥0}
     (n : ℕ) :
     ε • μ { ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω } ≤
       ENNReal.ofReal
@@ -169,7 +169,7 @@ we have `ε • μ {ε ≤ f* n} ≤ ∫ ω in {ε ≤ f* n}, f n` where `f* n 
 
 In some literature, the Doob's maximal inequality refers to what we call Doob's Lp inequality
 (which is a corollary of this lemma and will be proved in an upcomming PR). -/
-theorem maximal_ineq [IsFiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnonneg : 0 ≤ f) {ε : ℝ≥0}
+theorem maximal_ineq [FiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnonneg : 0 ≤ f) {ε : ℝ≥0}
     (n : ℕ) :
     ε • μ { ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω } ≤
       ENNReal.ofReal

70fd9563

bump to nightly-2023-05-04-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/92c69b77c5a7dc0f7eeddb552508633305157caa

3d8894bd

Diff

@@ -71,7 +71,7 @@ theorem Submartingale.expected_stoppedValue_mono [SigmaFiniteFiltration μ 𝒢]
 /-- The converse direction of the optional stopping theorem, i.e. an adapted integrable process `f`
 is a submartingale if for all bounded stopping times `τ` and `π` such that `τ ≤ π`, the
 stopped value of `f` at `τ` has expectation smaller than its stopped value at `π`. -/
-theorem submartingaleOfExpectedStoppedValueMono [IsFiniteMeasure μ] (hadp : Adapted 𝒢 f)
+theorem submartingale_of_expected_stoppedValue_mono [IsFiniteMeasure μ] (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ)
     (hf :
       ∀ τ π : Ω → ℕ,
@@ -89,7 +89,7 @@ theorem submartingaleOfExpectedStoppedValueMono [IsFiniteMeasure μ] (hadp : Ada
     rwa [stopped_value_const, stopped_value_piecewise_const,
       integral_piecewise (𝒢.le _ _ hs) (hint _).IntegrableOn (hint _).IntegrableOn, ←
       integral_add_compl (𝒢.le _ _ hs) (hint j), add_le_add_iff_right] at hf
-#align measure_theory.submartingale_of_expected_stopped_value_mono MeasureTheory.submartingaleOfExpectedStoppedValueMono
+#align measure_theory.submartingale_of_expected_stopped_value_mono MeasureTheory.submartingale_of_expected_stoppedValue_mono
 
 /-- **The optional stopping theorem** (fair game theorem): an adapted integrable process `f`
 is a submartingale if and only if for all bounded stopping times `τ` and `π` such that `τ ≤ π`, the
@@ -102,7 +102,7 @@ theorem submartingale_iff_expected_stoppedValue_mono [IsFiniteMeasure μ] (hadp
           IsStoppingTime 𝒢 π →
             τ ≤ π → (∃ N, ∀ x, π x ≤ N) → μ[stoppedValue f τ] ≤ μ[stoppedValue f π] :=
   ⟨fun hf _ _ hτ hπ hle ⟨N, hN⟩ => hf.expected_stoppedValue_mono hτ hπ hle hN,
-    submartingaleOfExpectedStoppedValueMono hadp hint⟩
+    submartingale_of_expected_stoppedValue_mono hadp hint⟩
 #align measure_theory.submartingale_iff_expected_stopped_value_mono MeasureTheory.submartingale_iff_expected_stoppedValue_mono
 
 /-- The stopped process of a submartingale with respect to a stopping time is a submartingale. -/

70fd9563

bump to nightly-2023-03-17-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

c85864d4

Diff

@@ -52,7 +52,7 @@ theorem Submartingale.expected_stoppedValue_mono [SigmaFiniteFiltration μ 𝒢]
       by
       intro i
       refine' (hτ i).inter _
-      convert (hπ i).compl
+      convert(hπ i).compl
       ext x
       simpa
     rw [integral_finset_sum]

70fd9563

bump to nightly-2023-02-27-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

49ff026a

Diff

@@ -30,7 +30,7 @@ This file also contains Doob's maximal inequality: given a non-negative submarti
  -/
 
 
-open NNReal Ennreal MeasureTheory ProbabilityTheory
+open NNReal ENNReal MeasureTheory ProbabilityTheory
 
 namespace MeasureTheory
 
@@ -130,7 +130,7 @@ open Finset
 theorem smul_le_stoppedValue_hitting [IsFiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) {ε : ℝ≥0}
     (n : ℕ) :
     ε • μ { ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω } ≤
-      Ennreal.ofReal
+      ENNReal.ofReal
         (∫ ω in { ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω },
           stoppedValue f (hitting f { y : ℝ | ↑ε ≤ y } 0 n) ω ∂μ) :=
   by
@@ -158,10 +158,10 @@ theorem smul_le_stoppedValue_hitting [IsFiniteMeasure μ] (hsub : Submartingale
       (integrable.integrable_on
         (hsub.integrable_stopped_value (hitting_is_stopping_time hsub.adapted measurableSet_Ici)
           hitting_le))
-  rw [Ennreal.le_ofReal_iff_toReal_le, Ennreal.toReal_smul]
+  rw [ENNReal.le_ofReal_iff_toReal_le, ENNReal.toReal_smul]
   · exact h
-  · exact Ennreal.mul_ne_top (by simp) (measure_ne_top _ _)
-  · exact le_trans (mul_nonneg ε.coe_nonneg Ennreal.toReal_nonneg) h
+  · exact ENNReal.mul_ne_top (by simp) (measure_ne_top _ _)
+  · exact le_trans (mul_nonneg ε.coe_nonneg ENNReal.toReal_nonneg) h
 #align measure_theory.smul_le_stopped_value_hitting MeasureTheory.smul_le_stoppedValue_hitting
 
 /-- **Doob's maximal inequality**: Given a non-negative submartingale `f`, for all `ε : ℝ≥0`,
@@ -172,26 +172,26 @@ In some literature, the Doob's maximal inequality refers to what we call Doob's
 theorem maximal_ineq [IsFiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnonneg : 0 ≤ f) {ε : ℝ≥0}
     (n : ℕ) :
     ε • μ { ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω } ≤
-      Ennreal.ofReal
+      ENNReal.ofReal
         (∫ ω in { ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω },
           f n ω ∂μ) :=
   by
   suffices
     ε • μ { ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω } +
-        Ennreal.ofReal
+        ENNReal.ofReal
           (∫ ω in { ω | ((range (n + 1)).sup' nonempty_range_succ fun k => f k ω) < ε }, f n ω ∂μ) ≤
-      Ennreal.ofReal (μ[f n])
+      ENNReal.ofReal (μ[f n])
     by
     have hadd :
-      Ennreal.ofReal (∫ ω, f n ω ∂μ) =
-        Ennreal.ofReal
+      ENNReal.ofReal (∫ ω, f n ω ∂μ) =
+        ENNReal.ofReal
             (∫ ω in { ω | ↑ε ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω },
               f n ω ∂μ) +
-          Ennreal.ofReal
+          ENNReal.ofReal
             (∫ ω in { ω | ((range (n + 1)).sup' nonempty_range_succ fun k => f k ω) < ↑ε },
               f n ω ∂μ) :=
       by
-      rw [← Ennreal.ofReal_add, ← integral_union]
+      rw [← ENNReal.ofReal_add, ← integral_union]
       · conv_lhs => rw [← integral_univ]
         convert rfl
         ext ω
@@ -208,22 +208,22 @@ theorem maximal_ineq [IsFiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnon
             measurable_const
       exacts[(hsub.integrable _).IntegrableOn, (hsub.integrable _).IntegrableOn,
         integral_nonneg (hnonneg _), integral_nonneg (hnonneg _)]
-    rwa [hadd, Ennreal.add_le_add_iff_right Ennreal.ofReal_ne_top] at this
+    rwa [hadd, ENNReal.add_le_add_iff_right ENNReal.ofReal_ne_top] at this
   calc
     ε • μ { ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω } +
-          Ennreal.ofReal
+          ENNReal.ofReal
             (∫ ω in { ω | ((range (n + 1)).sup' nonempty_range_succ fun k => f k ω) < ε },
               f n ω ∂μ) ≤
-        Ennreal.ofReal
+        ENNReal.ofReal
             (∫ ω in { ω | (ε : ℝ) ≤ (range (n + 1)).sup' nonempty_range_succ fun k => f k ω },
               stopped_value f (hitting f { y : ℝ | ↑ε ≤ y } 0 n) ω ∂μ) +
-          Ennreal.ofReal
+          ENNReal.ofReal
             (∫ ω in { ω | ((range (n + 1)).sup' nonempty_range_succ fun k => f k ω) < ε },
               stopped_value f (hitting f { y : ℝ | ↑ε ≤ y } 0 n) ω ∂μ) :=
       by
       refine'
         add_le_add (smul_le_stopped_value_hitting hsub _)
-          (Ennreal.ofReal_le_ofReal
+          (ENNReal.ofReal_le_ofReal
             (set_integral_mono_on (hsub.integrable n).IntegrableOn
               (integrable.integrable_on
                 (hsub.integrable_stopped_value
@@ -244,9 +244,9 @@ theorem maximal_ineq [IsFiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnon
           False.elim
             ((not_le.2 hω) ((le_sup'_iff _).2 ⟨m, mem_range.2 (Nat.lt_succ_of_le hm.2), hεm⟩))
       simp_rw [stopped_value, this]
-    _ = Ennreal.ofReal (∫ ω, stopped_value f (hitting f { y : ℝ | ↑ε ≤ y } 0 n) ω ∂μ) :=
+    _ = ENNReal.ofReal (∫ ω, stopped_value f (hitting f { y : ℝ | ↑ε ≤ y } 0 n) ω ∂μ) :=
       by
-      rw [← Ennreal.ofReal_add, ← integral_union]
+      rw [← ENNReal.ofReal_add, ← integral_union]
       · conv_rhs => rw [← integral_univ]
         convert rfl
         ext ω
@@ -272,9 +272,9 @@ theorem maximal_ineq [IsFiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnon
             (hsub.integrable_stopped_value (hitting_is_stopping_time hsub.adapted measurableSet_Ici)
               hitting_le)
       exacts[integral_nonneg fun x => hnonneg _ _, integral_nonneg fun x => hnonneg _ _]
-    _ ≤ Ennreal.ofReal (μ[f n]) :=
+    _ ≤ ENNReal.ofReal (μ[f n]) :=
       by
-      refine' Ennreal.ofReal_le_ofReal _
+      refine' ENNReal.ofReal_le_ofReal _
       rw [← stopped_value_const f n]
       exact
         hsub.expected_stopped_value_mono (hitting_is_stopping_time hsub.adapted measurableSet_Ici)

70fd9563

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

70fd9563

chore: replace set_integral with setIntegral (#12215)

Done with a global search and replace, and then (to fix the #align lines), replace (#align \S*)setIntegral with $1set_integral.

f4b4298b

Diff

@@ -35,7 +35,7 @@ variable {Ω : Type*} {m0 : MeasurableSpace Ω} {μ : Measure Ω} {𝒢 : Filtra
   {τ π : Ω → ℕ}
 
 -- We may generalize the below lemma to functions taking value in a `NormedLatticeAddCommGroup`.
--- Similarly, generalize `(Super/Sub)martingale.set_integral_le`.
+-- Similarly, generalize `(Super/Sub)martingale.setIntegral_le`.
 /-- Given a submartingale `f` and bounded stopping times `τ` and `π` such that `τ ≤ π`, the
 expectation of `stoppedValue f τ` is less than or equal to the expectation of `stoppedValue f π`.
 This is the forward direction of the optional stopping theorem. -/
@@ -53,7 +53,7 @@ theorem Submartingale.expected_stoppedValue_mono [SigmaFiniteFiltration μ 𝒢]
     rw [integral_finset_sum]
     · refine' Finset.sum_nonneg fun i _ => _
       rw [integral_indicator (𝒢.le _ _ (this _)), integral_sub', sub_nonneg]
-      · exact hf.set_integral_le (Nat.le_succ i) (this _)
+      · exact hf.setIntegral_le (Nat.le_succ i) (this _)
       · exact (hf.integrable _).integrableOn
       · exact (hf.integrable _).integrableOn
     intro i _
@@ -70,7 +70,7 @@ theorem submartingale_of_expected_stoppedValue_mono [IsFiniteMeasure μ] (hadp :
     (hint : ∀ i, Integrable (f i) μ) (hf : ∀ τ π : Ω → ℕ, IsStoppingTime 𝒢 τ → IsStoppingTime 𝒢 π →
       τ ≤ π → (∃ N, ∀ ω, π ω ≤ N) → μ[stoppedValue f τ] ≤ μ[stoppedValue f π]) :
     Submartingale f 𝒢 μ := by
-  refine' submartingale_of_set_integral_le hadp hint fun i j hij s hs => _
+  refine' submartingale_of_setIntegral_le hadp hint fun i j hij s hs => _
   classical
   specialize hf (s.piecewise (fun _ => i) fun _ => j) _ (isStoppingTime_piecewise_const hij hs)
     (isStoppingTime_const 𝒢 j) (fun x => (ite_le_sup _ _ (x ∈ s)).trans (max_eq_right hij).le)
@@ -123,7 +123,7 @@ theorem smul_le_stoppedValue_hitting [IsFiniteMeasure μ] (hsub : Submartingale
     exact
       let ⟨j, hj₁, hj₂⟩ := hx
       ⟨j, hj₁, hj₂⟩
-  have h := set_integral_ge_of_const_le (measurableSet_le measurable_const
+  have h := setIntegral_ge_of_const_le (measurableSet_le measurable_const
     (Finset.measurable_range_sup'' fun n _ => (hsub.stronglyMeasurable n).measurable.le (𝒢.le n)))
       (measure_ne_top _ _) this (Integrable.integrableOn (hsub.integrable_stoppedValue
         (hitting_isStoppingTime hsub.adapted measurableSet_Ici) hitting_le))
@@ -178,7 +178,7 @@ theorem maximal_ineq [IsFiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnon
           (∫ ω in {ω | ((range (n + 1)).sup' nonempty_range_succ fun k => f k ω) < ε},
             stoppedValue f (hitting f {y : ℝ | ↑ε ≤ y} 0 n) ω ∂μ) := by
       refine' add_le_add (smul_le_stoppedValue_hitting hsub _)
-        (ENNReal.ofReal_le_ofReal (set_integral_mono_on (hsub.integrable n).integrableOn
+        (ENNReal.ofReal_le_ofReal (setIntegral_mono_on (hsub.integrable n).integrableOn
           (Integrable.integrableOn (hsub.integrable_stoppedValue
             (hitting_isStoppingTime hsub.adapted measurableSet_Ici) hitting_le))
               (measurableSet_lt (Finset.measurable_range_sup'' fun n _ =>

70fd9563

chore: Rename coe_nat/coe_int/coe_rat to natCast/intCast/ratCast (#11499)

This is less exhaustive than its sibling #11486 because edge cases are harder to classify. No fundamental difficulty, just me being a bit fast and lazy.

Reduce the diff of #11203

b2af0d13

Diff

@@ -186,7 +186,7 @@ theorem maximal_ineq [IsFiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnon
       intro ω hω
       rw [Set.mem_setOf_eq] at hω
       have : hitting f {y : ℝ | ↑ε ≤ y} 0 n ω = n := by
-        classical simp only [hitting, Set.mem_setOf_eq, exists_prop, Pi.coe_nat, Nat.cast_id,
+        classical simp only [hitting, Set.mem_setOf_eq, exists_prop, Pi.natCast_def, Nat.cast_id,
           ite_eq_right_iff, forall_exists_index, and_imp]
         intro m hm hεm
         exact False.elim

70fd9563

chore(*): use α → β instead of ∀ _ : α, β (#9529)

5618e431

Diff

@@ -215,7 +215,7 @@ theorem maximal_ineq [IsFiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnon
       refine' ENNReal.ofReal_le_ofReal _
       rw [← stoppedValue_const f n]
       exact hsub.expected_stoppedValue_mono (hitting_isStoppingTime hsub.adapted measurableSet_Ici)
-        (isStoppingTime_const _ _) (fun ω => hitting_le ω) (fun _ => le_rfl : ∀ _, n ≤ n)
+        (isStoppingTime_const _ _) (fun ω => hitting_le ω) (fun _ => le_refl n)
 #align measure_theory.maximal_ineq MeasureTheory.maximal_ineq
 
 end Maximal

70fd9563

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.

32de3f67

Diff

@@ -31,7 +31,7 @@ open scoped NNReal ENNReal MeasureTheory ProbabilityTheory
 
 namespace MeasureTheory
 
-variable {Ω : Type _} {m0 : MeasurableSpace Ω} {μ : Measure Ω} {𝒢 : Filtration ℕ m0} {f : ℕ → Ω → ℝ}
+variable {Ω : Type*} {m0 : MeasurableSpace Ω} {μ : Measure Ω} {𝒢 : Filtration ℕ m0} {f : ℕ → Ω → ℝ}
   {τ π : Ω → ℕ}
 
 -- We may generalize the below lemma to functions taking value in a `NormedLatticeAddCommGroup`.

70fd9563

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Kexing Ying. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
-
-! This file was ported from Lean 3 source module probability.martingale.optional_stopping
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Probability.Process.HittingTime
 import Mathlib.Probability.Martingale.Basic
 
+#align_import probability.martingale.optional_stopping from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+
 /-! # Optional stopping theorem (fair game theorem)
 
 The optional stopping theorem states that an adapted integrable process `f` is a submartingale if

70fd9563

feat: port Probability.Martingale.OptionalStopping (#5274)

51aa827c

`probability.martingale.optional_stopping` ⟷ `Mathlib.Probability.Martingale.OptionalStopping`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 1007

probability.martingale.optional_stopping ⟷ Mathlib.Probability.Martingale.OptionalStopping

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 1007

`probability.martingale.optional_stopping` ⟷ `Mathlib.Probability.Martingale.OptionalStopping`