probability.martingale.basic ⟷ Mathlib.Probability.Martingale.Basic

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

@@ -136,14 +136,14 @@ theorem integrable (hf : Martingale f ℱ μ) (i : ι) : Integrable (f i) μ :=
 #align measure_theory.martingale.integrable MeasureTheory.Martingale.integrable
 -/
 
-#print MeasureTheory.Martingale.set_integral_eq /-
-theorem set_integral_eq [SigmaFiniteFiltration μ ℱ] (hf : Martingale f ℱ μ) {i j : ι} (hij : i ≤ j)
+#print MeasureTheory.Martingale.setIntegral_eq /-
+theorem setIntegral_eq [SigmaFiniteFiltration μ ℱ] (hf : Martingale f ℱ μ) {i j : ι} (hij : i ≤ j)
     {s : Set Ω} (hs : measurable_set[ℱ i] s) : ∫ ω in s, f i ω ∂μ = ∫ ω in s, f j ω ∂μ :=
   by
   rw [← @set_integral_condexp _ _ _ _ _ (ℱ i) m0 _ _ _ (ℱ.le i) _ (hf.integrable j) hs]
   refine' set_integral_congr_ae (ℱ.le i s hs) _
   filter_upwards [hf.2 i j hij] with _ heq _ using HEq.symm
-#align measure_theory.martingale.set_integral_eq MeasureTheory.Martingale.set_integral_eq
+#align measure_theory.martingale.set_integral_eq MeasureTheory.Martingale.setIntegral_eq
 -/
 
 #print MeasureTheory.Martingale.add /-
@@ -235,15 +235,15 @@ theorem condexp_ae_le [LE E] (hf : Supermartingale f ℱ μ) {i j : ι} (hij : i
 #align measure_theory.supermartingale.condexp_ae_le MeasureTheory.Supermartingale.condexp_ae_le
 -/
 
-#print MeasureTheory.Supermartingale.set_integral_le /-
-theorem set_integral_le [SigmaFiniteFiltration μ ℱ] {f : ι → Ω → ℝ} (hf : Supermartingale f ℱ μ)
+#print MeasureTheory.Supermartingale.setIntegral_le /-
+theorem setIntegral_le [SigmaFiniteFiltration μ ℱ] {f : ι → Ω → ℝ} (hf : Supermartingale f ℱ μ)
     {i j : ι} (hij : i ≤ j) {s : Set Ω} (hs : measurable_set[ℱ i] s) :
     ∫ ω in s, f j ω ∂μ ≤ ∫ ω in s, f i ω ∂μ :=
   by
   rw [← set_integral_condexp (ℱ.le i) (hf.integrable j) hs]
   refine' set_integral_mono_ae integrable_condexp.integrable_on (hf.integrable i).IntegrableOn _
   filter_upwards [hf.2.1 i j hij] with _ heq using HEq
-#align measure_theory.supermartingale.set_integral_le MeasureTheory.Supermartingale.set_integral_le
+#align measure_theory.supermartingale.set_integral_le MeasureTheory.Supermartingale.setIntegral_le
 -/
 
 #print MeasureTheory.Supermartingale.add /-
@@ -338,15 +338,15 @@ theorem neg [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Submar
 #align measure_theory.submartingale.neg MeasureTheory.Submartingale.neg
 -/
 
-#print MeasureTheory.Submartingale.set_integral_le /-
+#print MeasureTheory.Submartingale.setIntegral_le /-
 /-- The converse of this lemma is `measure_theory.submartingale_of_set_integral_le`. -/
-theorem set_integral_le [SigmaFiniteFiltration μ ℱ] {f : ι → Ω → ℝ} (hf : Submartingale f ℱ μ)
+theorem setIntegral_le [SigmaFiniteFiltration μ ℱ] {f : ι → Ω → ℝ} (hf : Submartingale f ℱ μ)
     {i j : ι} (hij : i ≤ j) {s : Set Ω} (hs : measurable_set[ℱ i] s) :
     ∫ ω in s, f i ω ∂μ ≤ ∫ ω in s, f j ω ∂μ :=
   by
   rw [← neg_le_neg_iff, ← integral_neg, ← integral_neg]
   exact supermartingale.set_integral_le hf.neg hij hs
-#align measure_theory.submartingale.set_integral_le MeasureTheory.Submartingale.set_integral_le
+#align measure_theory.submartingale.set_integral_le MeasureTheory.Submartingale.setIntegral_le
 -/
 
 #print MeasureTheory.Submartingale.sub_supermartingale /-
@@ -394,8 +394,8 @@ end Submartingale
 
 section Submartingale
 
-#print MeasureTheory.submartingale_of_set_integral_le /-
-theorem submartingale_of_set_integral_le [IsFiniteMeasure μ] {f : ι → Ω → ℝ} (hadp : Adapted ℱ f)
+#print MeasureTheory.submartingale_of_setIntegral_le /-
+theorem submartingale_of_setIntegral_le [IsFiniteMeasure μ] {f : ι → Ω → ℝ} (hadp : Adapted ℱ f)
     (hint : ∀ i, Integrable (f i) μ)
     (hf :
       ∀ i j : ι,
@@ -415,7 +415,7 @@ theorem submartingale_of_set_integral_le [IsFiniteMeasure μ] {f : ι → Ω →
   rwa [← set_integral_trim _ (strongly_measurable_condexp.sub <| hadp i) hs,
     integral_sub' integrable_condexp.integrable_on (hint i).IntegrableOn, sub_nonneg,
     set_integral_condexp (ℱ.le i) (hint j) hs]
-#align measure_theory.submartingale_of_set_integral_le MeasureTheory.submartingale_of_set_integral_le
+#align measure_theory.submartingale_of_set_integral_le MeasureTheory.submartingale_of_setIntegral_le
 -/
 
 #print MeasureTheory.submartingale_of_condexp_sub_nonneg /-
@@ -533,8 +533,8 @@ section Nat
 
 variable {𝒢 : Filtration ℕ m0}
 
-#print MeasureTheory.submartingale_of_set_integral_le_succ /-
-theorem submartingale_of_set_integral_le_succ [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
+#print MeasureTheory.submartingale_of_setIntegral_le_succ /-
+theorem submartingale_of_setIntegral_le_succ [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
     (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
     (hf : ∀ i, ∀ s : Set Ω, measurable_set[𝒢 i] s → ∫ ω in s, f i ω ∂μ ≤ ∫ ω in s, f (i + 1) ω ∂μ) :
     Submartingale f 𝒢 μ :=
@@ -543,29 +543,29 @@ theorem submartingale_of_set_integral_le_succ [IsFiniteMeasure μ] {f : ℕ →
   induction' hij with k hk₁ hk₂
   · exact le_rfl
   · exact le_trans hk₂ (hf k s (𝒢.mono hk₁ _ hs))
-#align measure_theory.submartingale_of_set_integral_le_succ MeasureTheory.submartingale_of_set_integral_le_succ
+#align measure_theory.submartingale_of_set_integral_le_succ MeasureTheory.submartingale_of_setIntegral_le_succ
 -/
 
-#print MeasureTheory.supermartingale_of_set_integral_succ_le /-
-theorem supermartingale_of_set_integral_succ_le [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
+#print MeasureTheory.supermartingale_of_setIntegral_succ_le /-
+theorem supermartingale_of_setIntegral_succ_le [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
     (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
     (hf : ∀ i, ∀ s : Set Ω, measurable_set[𝒢 i] s → ∫ ω in s, f (i + 1) ω ∂μ ≤ ∫ ω in s, f i ω ∂μ) :
     Supermartingale f 𝒢 μ := by
   rw [← neg_neg f]
   refine' (submartingale_of_set_integral_le_succ hadp.neg (fun i => (hint i).neg) _).neg
   simpa only [integral_neg, Pi.neg_apply, neg_le_neg_iff]
-#align measure_theory.supermartingale_of_set_integral_succ_le MeasureTheory.supermartingale_of_set_integral_succ_le
+#align measure_theory.supermartingale_of_set_integral_succ_le MeasureTheory.supermartingale_of_setIntegral_succ_le
 -/
 
-#print MeasureTheory.martingale_of_set_integral_eq_succ /-
-theorem martingale_of_set_integral_eq_succ [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
+#print MeasureTheory.martingale_of_setIntegral_eq_succ /-
+theorem martingale_of_setIntegral_eq_succ [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ)
     (hf : ∀ i, ∀ s : Set Ω, measurable_set[𝒢 i] s → ∫ ω in s, f i ω ∂μ = ∫ ω in s, f (i + 1) ω ∂μ) :
     Martingale f 𝒢 μ :=
   martingale_iff.2
-    ⟨supermartingale_of_set_integral_succ_le hadp hint fun i s hs => (hf i s hs).ge,
-      submartingale_of_set_integral_le_succ hadp hint fun i s hs => (hf i s hs).le⟩
-#align measure_theory.martingale_of_set_integral_eq_succ MeasureTheory.martingale_of_set_integral_eq_succ
+    ⟨supermartingale_of_setIntegral_succ_le hadp hint fun i s hs => (hf i s hs).ge,
+      submartingale_of_setIntegral_le_succ hadp hint fun i s hs => (hf i s hs).le⟩
+#align measure_theory.martingale_of_set_integral_eq_succ MeasureTheory.martingale_of_setIntegral_eq_succ
 -/
 
 #print MeasureTheory.submartingale_nat /-

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

@@ -723,7 +723,7 @@ theorem Submartingale.sum_mul_sub [IsFiniteMeasure μ] {R : ℝ} {ξ f : ℕ →
     by
     intro m
     refine' Finset.stronglyMeasurable_sum' _ fun i hi => _
-    rw [Finset.mem_range] at hi 
+    rw [Finset.mem_range] at hi
     exact
       (hξ.strongly_measurable_le hi.le).mul
         ((hf.adapted.strongly_measurable_le (Nat.succ_le_of_lt hi)).sub

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

@@ -483,7 +483,7 @@ theorem smul_nonneg {f : ι → Ω → F} {c : ℝ} (hc : 0 ≤ c) (hf : Superma
   refine' (condexp_smul c (f j)).le.trans _
   filter_upwards [hf.2.1 i j hij] with _ hle
   simp_rw [Pi.smul_apply]
-  exact smul_le_smul_of_nonneg hle hc
+  exact smul_le_smul_of_nonneg_left hle hc
 #align measure_theory.supermartingale.smul_nonneg MeasureTheory.Supermartingale.smul_nonneg
 -/
 

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Rémy Degenne. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne, Kexing Ying
 -/
-import Mathbin.Probability.Notation
-import Mathbin.Probability.Process.Stopping
+import Probability.Notation
+import Probability.Process.Stopping
 
 #align_import probability.martingale.basic from "leanprover-community/mathlib"@"f2ad3645af9effcdb587637dc28a6074edc813f9"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Rémy Degenne. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne, Kexing Ying
-
-! This file was ported from Lean 3 source module probability.martingale.basic
-! 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.Probability.Notation
 import Mathbin.Probability.Process.Stopping
 
+#align_import probability.martingale.basic from "leanprover-community/mathlib"@"f2ad3645af9effcdb587637dc28a6074edc813f9"
+
 /-!
 # Martingales
 

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, Kexing Ying
 
 ! This file was ported from Lean 3 source module probability.martingale.basic
-! 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.Process.Stopping
 /-!
 # Martingales
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A family of functions `f : ι → Ω → E` is a martingale with respect to a filtration `ℱ` if every
 `f i` is integrable, `f` is adapted with respect to `ℱ` and for all `i ≤ j`,
 `μ[f j | ℱ i] =ᵐ[μ] f i`. On the other hand, `f : ι → Ω → E` is said to be a supermartingale

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

@@ -491,7 +491,7 @@ theorem smul_nonneg {f : ι → Ω → F} {c : ℝ} (hc : 0 ≤ c) (hf : Superma
 theorem smul_nonpos {f : ι → Ω → F} {c : ℝ} (hc : c ≤ 0) (hf : Supermartingale f ℱ μ) :
     Submartingale (c • f) ℱ μ :=
   by
-  rw [← neg_neg c, (by ext (i x); simp : - -c • f = -(-c • f))]
+  rw [← neg_neg c, (by ext i x; simp : - -c • f = -(-c • f))]
   exact (hf.smul_nonneg <| neg_nonneg.2 hc).neg
 #align measure_theory.supermartingale.smul_nonpos MeasureTheory.Supermartingale.smul_nonpos
 -/
@@ -511,7 +511,7 @@ variable {F : Type _} [NormedLatticeAddCommGroup F] [NormedSpace ℝ F] [Complet
 theorem smul_nonneg {f : ι → Ω → F} {c : ℝ} (hc : 0 ≤ c) (hf : Submartingale f ℱ μ) :
     Submartingale (c • f) ℱ μ :=
   by
-  rw [← neg_neg c, (by ext (i x); simp : - -c • f = -(c • -f))]
+  rw [← neg_neg c, (by ext i x; simp : - -c • f = -(c • -f))]
   exact supermartingale.neg (hf.neg.smul_nonneg hc)
 #align measure_theory.submartingale.smul_nonneg MeasureTheory.Submartingale.smul_nonneg
 -/
@@ -520,7 +520,7 @@ theorem smul_nonneg {f : ι → Ω → F} {c : ℝ} (hc : 0 ≤ c) (hf : Submart
 theorem smul_nonpos {f : ι → Ω → F} {c : ℝ} (hc : c ≤ 0) (hf : Submartingale f ℱ μ) :
     Supermartingale (c • f) ℱ μ :=
   by
-  rw [← neg_neg c, (by ext (i x); simp : - -c • f = -(-c • f))]
+  rw [← neg_neg c, (by ext i x; simp : - -c • f = -(-c • f))]
   exact (hf.smul_nonneg <| neg_nonneg.2 hc).neg
 #align measure_theory.submartingale.smul_nonpos MeasureTheory.Submartingale.smul_nonpos
 -/

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

@@ -50,13 +50,16 @@ namespace MeasureTheory
 variable {Ω E ι : Type _} [Preorder ι] {m0 : MeasurableSpace Ω} {μ : Measure Ω}
   [NormedAddCommGroup E] [NormedSpace ℝ E] [CompleteSpace E] {f g : ι → Ω → E} {ℱ : Filtration ι m0}
 
+#print MeasureTheory.Martingale /-
 /-- A family of functions `f : ι → Ω → E` is a martingale with respect to a filtration `ℱ` if `f`
 is adapted with respect to `ℱ` and for all `i ≤ j`, `μ[f j | ℱ i] =ᵐ[μ] f i`. -/
 def Martingale (f : ι → Ω → E) (ℱ : Filtration ι m0)
     (μ : Measure Ω := by exact MeasureTheory.MeasureSpace.volume) : Prop :=
   Adapted ℱ f ∧ ∀ i j, i ≤ j → μ[f j|ℱ i] =ᵐ[μ] f i
 #align measure_theory.martingale MeasureTheory.Martingale
+-/
 
+#print MeasureTheory.Supermartingale /-
 /-- A family of integrable functions `f : ι → Ω → E` is a supermartingale with respect to a
 filtration `ℱ` if `f` is adapted with respect to `ℱ` and for all `i ≤ j`,
 `μ[f j | ℱ.le i] ≤ᵐ[μ] f i`. -/
@@ -64,7 +67,9 @@ def Supermartingale [LE E] (f : ι → Ω → E) (ℱ : Filtration ι m0)
     (μ : Measure Ω := by exact MeasureTheory.MeasureSpace.volume) : Prop :=
   Adapted ℱ f ∧ (∀ i j, i ≤ j → μ[f j|ℱ i] ≤ᵐ[μ] f i) ∧ ∀ i, Integrable (f i) μ
 #align measure_theory.supermartingale MeasureTheory.Supermartingale
+-/
 
+#print MeasureTheory.Submartingale /-
 /-- A family of integrable functions `f : ι → Ω → E` is a submartingale with respect to a
 filtration `ℱ` if `f` is adapted with respect to `ℱ` and for all `i ≤ j`,
 `f i ≤ᵐ[μ] μ[f j | ℱ.le i]`. -/
@@ -72,12 +77,16 @@ def Submartingale [LE E] (f : ι → Ω → E) (ℱ : Filtration ι m0)
     (μ : Measure Ω := by exact MeasureTheory.MeasureSpace.volume) : Prop :=
   Adapted ℱ f ∧ (∀ i j, i ≤ j → f i ≤ᵐ[μ] μ[f j|ℱ i]) ∧ ∀ i, Integrable (f i) μ
 #align measure_theory.submartingale MeasureTheory.Submartingale
+-/
 
+#print MeasureTheory.martingale_const /-
 theorem martingale_const (ℱ : Filtration ι m0) (μ : Measure Ω) [IsFiniteMeasure μ] (x : E) :
     Martingale (fun _ _ => x) ℱ μ :=
   ⟨adapted_const ℱ _, fun i j hij => by rw [condexp_const (ℱ.le _)]⟩
 #align measure_theory.martingale_const MeasureTheory.martingale_const
+-/
 
+#print MeasureTheory.martingale_const_fun /-
 theorem martingale_const_fun [OrderBot ι] (ℱ : Filtration ι m0) (μ : Measure Ω) [IsFiniteMeasure μ]
     {f : Ω → E} (hf : strongly_measurable[ℱ ⊥] f) (hfint : Integrable f μ) :
     Martingale (fun _ => f) ℱ μ :=
@@ -86,36 +95,48 @@ theorem martingale_const_fun [OrderBot ι] (ℱ : Filtration ι m0) (μ : Measur
   rw [condexp_of_strongly_measurable (ℱ.le _) (hf.mono <| ℱ.mono bot_le) hfint]
   infer_instance
 #align measure_theory.martingale_const_fun MeasureTheory.martingale_const_fun
+-/
 
 variable (E)
 
+#print MeasureTheory.martingale_zero /-
 theorem martingale_zero (ℱ : Filtration ι m0) (μ : Measure Ω) : Martingale (0 : ι → Ω → E) ℱ μ :=
   ⟨adapted_zero E ℱ, fun i j hij => by rw [Pi.zero_apply, condexp_zero]; simp⟩
 #align measure_theory.martingale_zero MeasureTheory.martingale_zero
+-/
 
 variable {E}
 
 namespace Martingale
 
+#print MeasureTheory.Martingale.adapted /-
 @[protected]
 theorem adapted (hf : Martingale f ℱ μ) : Adapted ℱ f :=
   hf.1
 #align measure_theory.martingale.adapted MeasureTheory.Martingale.adapted
+-/
 
+#print MeasureTheory.Martingale.stronglyMeasurable /-
 @[protected]
 theorem stronglyMeasurable (hf : Martingale f ℱ μ) (i : ι) : strongly_measurable[ℱ i] (f i) :=
   hf.Adapted i
 #align measure_theory.martingale.strongly_measurable MeasureTheory.Martingale.stronglyMeasurable
+-/
 
+#print MeasureTheory.Martingale.condexp_ae_eq /-
 theorem condexp_ae_eq (hf : Martingale f ℱ μ) {i j : ι} (hij : i ≤ j) : μ[f j|ℱ i] =ᵐ[μ] f i :=
   hf.2 i j hij
 #align measure_theory.martingale.condexp_ae_eq MeasureTheory.Martingale.condexp_ae_eq
+-/
 
+#print MeasureTheory.Martingale.integrable /-
 @[protected]
 theorem integrable (hf : Martingale f ℱ μ) (i : ι) : Integrable (f i) μ :=
   integrable_condexp.congr (hf.condexp_ae_eq (le_refl i))
 #align measure_theory.martingale.integrable MeasureTheory.Martingale.integrable
+-/
 
+#print MeasureTheory.Martingale.set_integral_eq /-
 theorem set_integral_eq [SigmaFiniteFiltration μ ℱ] (hf : Martingale f ℱ μ) {i j : ι} (hij : i ≤ j)
     {s : Set Ω} (hs : measurable_set[ℱ i] s) : ∫ ω in s, f i ω ∂μ = ∫ ω in s, f j ω ∂μ :=
   by
@@ -123,72 +144,98 @@ theorem set_integral_eq [SigmaFiniteFiltration μ ℱ] (hf : Martingale f ℱ μ
   refine' set_integral_congr_ae (ℱ.le i s hs) _
   filter_upwards [hf.2 i j hij] with _ heq _ using HEq.symm
 #align measure_theory.martingale.set_integral_eq MeasureTheory.Martingale.set_integral_eq
+-/
 
+#print MeasureTheory.Martingale.add /-
 theorem add (hf : Martingale f ℱ μ) (hg : Martingale g ℱ μ) : Martingale (f + g) ℱ μ :=
   by
   refine' ⟨hf.adapted.add hg.adapted, fun i j hij => _⟩
   exact (condexp_add (hf.integrable j) (hg.integrable j)).trans ((hf.2 i j hij).add (hg.2 i j hij))
 #align measure_theory.martingale.add MeasureTheory.Martingale.add
+-/
 
+#print MeasureTheory.Martingale.neg /-
 theorem neg (hf : Martingale f ℱ μ) : Martingale (-f) ℱ μ :=
   ⟨hf.Adapted.neg, fun i j hij => (condexp_neg (f j)).trans (hf.2 i j hij).neg⟩
 #align measure_theory.martingale.neg MeasureTheory.Martingale.neg
+-/
 
+#print MeasureTheory.Martingale.sub /-
 theorem sub (hf : Martingale f ℱ μ) (hg : Martingale g ℱ μ) : Martingale (f - g) ℱ μ := by
   rw [sub_eq_add_neg]; exact hf.add hg.neg
 #align measure_theory.martingale.sub MeasureTheory.Martingale.sub
+-/
 
+#print MeasureTheory.Martingale.smul /-
 theorem smul (c : ℝ) (hf : Martingale f ℱ μ) : Martingale (c • f) ℱ μ :=
   by
   refine' ⟨hf.adapted.smul c, fun i j hij => _⟩
   refine' (condexp_smul c (f j)).trans ((hf.2 i j hij).mono fun x hx => _)
   rw [Pi.smul_apply, hx, Pi.smul_apply, Pi.smul_apply]
 #align measure_theory.martingale.smul MeasureTheory.Martingale.smul
+-/
 
+#print MeasureTheory.Martingale.supermartingale /-
 theorem supermartingale [Preorder E] (hf : Martingale f ℱ μ) : Supermartingale f ℱ μ :=
   ⟨hf.1, fun i j hij => (hf.2 i j hij).le, fun i => hf.Integrable i⟩
 #align measure_theory.martingale.supermartingale MeasureTheory.Martingale.supermartingale
+-/
 
+#print MeasureTheory.Martingale.submartingale /-
 theorem submartingale [Preorder E] (hf : Martingale f ℱ μ) : Submartingale f ℱ μ :=
   ⟨hf.1, fun i j hij => (hf.2 i j hij).symm.le, fun i => hf.Integrable i⟩
 #align measure_theory.martingale.submartingale MeasureTheory.Martingale.submartingale
+-/
 
 end Martingale
 
+#print MeasureTheory.martingale_iff /-
 theorem martingale_iff [PartialOrder E] :
     Martingale f ℱ μ ↔ Supermartingale f ℱ μ ∧ Submartingale f ℱ μ :=
   ⟨fun hf => ⟨hf.Supermartingale, hf.Submartingale⟩, fun ⟨hf₁, hf₂⟩ =>
     ⟨hf₁.1, fun i j hij => (hf₁.2.1 i j hij).antisymm (hf₂.2.1 i j hij)⟩⟩
 #align measure_theory.martingale_iff MeasureTheory.martingale_iff
+-/
 
+#print MeasureTheory.martingale_condexp /-
 theorem martingale_condexp (f : Ω → E) (ℱ : Filtration ι m0) (μ : Measure Ω)
     [SigmaFiniteFiltration μ ℱ] : Martingale (fun i => μ[f|ℱ i]) ℱ μ :=
   ⟨fun i => stronglyMeasurable_condexp, fun i j hij => condexp_condexp_of_le (ℱ.mono hij) (ℱ.le j)⟩
 #align measure_theory.martingale_condexp MeasureTheory.martingale_condexp
+-/
 
 namespace Supermartingale
 
+#print MeasureTheory.Supermartingale.adapted /-
 @[protected]
 theorem adapted [LE E] (hf : Supermartingale f ℱ μ) : Adapted ℱ f :=
   hf.1
 #align measure_theory.supermartingale.adapted MeasureTheory.Supermartingale.adapted
+-/
 
+#print MeasureTheory.Supermartingale.stronglyMeasurable /-
 @[protected]
 theorem stronglyMeasurable [LE E] (hf : Supermartingale f ℱ μ) (i : ι) :
     strongly_measurable[ℱ i] (f i) :=
   hf.Adapted i
 #align measure_theory.supermartingale.strongly_measurable MeasureTheory.Supermartingale.stronglyMeasurable
+-/
 
+#print MeasureTheory.Supermartingale.integrable /-
 @[protected]
 theorem integrable [LE E] (hf : Supermartingale f ℱ μ) (i : ι) : Integrable (f i) μ :=
   hf.2.2 i
 #align measure_theory.supermartingale.integrable MeasureTheory.Supermartingale.integrable
+-/
 
+#print MeasureTheory.Supermartingale.condexp_ae_le /-
 theorem condexp_ae_le [LE E] (hf : Supermartingale f ℱ μ) {i j : ι} (hij : i ≤ j) :
     μ[f j|ℱ i] ≤ᵐ[μ] f i :=
   hf.2.1 i j hij
 #align measure_theory.supermartingale.condexp_ae_le MeasureTheory.Supermartingale.condexp_ae_le
+-/
 
+#print MeasureTheory.Supermartingale.set_integral_le /-
 theorem set_integral_le [SigmaFiniteFiltration μ ℱ] {f : ι → Ω → ℝ} (hf : Supermartingale f ℱ μ)
     {i j : ι} (hij : i ≤ j) {s : Set Ω} (hs : measurable_set[ℱ i] s) :
     ∫ ω in s, f j ω ∂μ ≤ ∫ ω in s, f i ω ∂μ :=
@@ -197,7 +244,9 @@ theorem set_integral_le [SigmaFiniteFiltration μ ℱ] {f : ι → Ω → ℝ} (
   refine' set_integral_mono_ae integrable_condexp.integrable_on (hf.integrable i).IntegrableOn _
   filter_upwards [hf.2.1 i j hij] with _ heq using HEq
 #align measure_theory.supermartingale.set_integral_le MeasureTheory.Supermartingale.set_integral_le
+-/
 
+#print MeasureTheory.Supermartingale.add /-
 theorem add [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Supermartingale f ℱ μ)
     (hg : Supermartingale g ℱ μ) : Supermartingale (f + g) ℱ μ :=
   by
@@ -207,12 +256,16 @@ theorem add [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Superm
   intros
   refine' add_le_add _ _ <;> assumption
 #align measure_theory.supermartingale.add MeasureTheory.Supermartingale.add
+-/
 
+#print MeasureTheory.Supermartingale.add_martingale /-
 theorem add_martingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)]
     (hf : Supermartingale f ℱ μ) (hg : Martingale g ℱ μ) : Supermartingale (f + g) ℱ μ :=
   hf.add hg.Supermartingale
 #align measure_theory.supermartingale.add_martingale MeasureTheory.Supermartingale.add_martingale
+-/
 
+#print MeasureTheory.Supermartingale.neg /-
 theorem neg [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Supermartingale f ℱ μ) :
     Submartingale (-f) ℱ μ :=
   by
@@ -221,32 +274,42 @@ theorem neg [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Superm
   filter_upwards [hf.2.1 i j hij] with _ _
   simpa
 #align measure_theory.supermartingale.neg MeasureTheory.Supermartingale.neg
+-/
 
 end Supermartingale
 
 namespace Submartingale
 
+#print MeasureTheory.Submartingale.adapted /-
 @[protected]
 theorem adapted [LE E] (hf : Submartingale f ℱ μ) : Adapted ℱ f :=
   hf.1
 #align measure_theory.submartingale.adapted MeasureTheory.Submartingale.adapted
+-/
 
+#print MeasureTheory.Submartingale.stronglyMeasurable /-
 @[protected]
 theorem stronglyMeasurable [LE E] (hf : Submartingale f ℱ μ) (i : ι) :
     strongly_measurable[ℱ i] (f i) :=
   hf.Adapted i
 #align measure_theory.submartingale.strongly_measurable MeasureTheory.Submartingale.stronglyMeasurable
+-/
 
+#print MeasureTheory.Submartingale.integrable /-
 @[protected]
 theorem integrable [LE E] (hf : Submartingale f ℱ μ) (i : ι) : Integrable (f i) μ :=
   hf.2.2 i
 #align measure_theory.submartingale.integrable MeasureTheory.Submartingale.integrable
+-/
 
+#print MeasureTheory.Submartingale.ae_le_condexp /-
 theorem ae_le_condexp [LE E] (hf : Submartingale f ℱ μ) {i j : ι} (hij : i ≤ j) :
     f i ≤ᵐ[μ] μ[f j|ℱ i] :=
   hf.2.1 i j hij
 #align measure_theory.submartingale.ae_le_condexp MeasureTheory.Submartingale.ae_le_condexp
+-/
 
+#print MeasureTheory.Submartingale.add /-
 theorem add [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Submartingale f ℱ μ)
     (hg : Submartingale g ℱ μ) : Submartingale (f + g) ℱ μ :=
   by
@@ -256,12 +319,16 @@ theorem add [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Submar
   intros
   refine' add_le_add _ _ <;> assumption
 #align measure_theory.submartingale.add MeasureTheory.Submartingale.add
+-/
 
+#print MeasureTheory.Submartingale.add_martingale /-
 theorem add_martingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Submartingale f ℱ μ)
     (hg : Martingale g ℱ μ) : Submartingale (f + g) ℱ μ :=
   hf.add hg.Submartingale
 #align measure_theory.submartingale.add_martingale MeasureTheory.Submartingale.add_martingale
+-/
 
+#print MeasureTheory.Submartingale.neg /-
 theorem neg [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Submartingale f ℱ μ) :
     Supermartingale (-f) ℱ μ :=
   by
@@ -269,7 +336,9 @@ theorem neg [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Submar
   filter_upwards [hf.2.1 i j hij] with _ _
   simpa
 #align measure_theory.submartingale.neg MeasureTheory.Submartingale.neg
+-/
 
+#print MeasureTheory.Submartingale.set_integral_le /-
 /-- The converse of this lemma is `measure_theory.submartingale_of_set_integral_le`. -/
 theorem set_integral_le [SigmaFiniteFiltration μ ℱ] {f : ι → Ω → ℝ} (hf : Submartingale f ℱ μ)
     {i j : ι} (hij : i ≤ j) {s : Set Ω} (hs : measurable_set[ℱ i] s) :
@@ -278,17 +347,23 @@ theorem set_integral_le [SigmaFiniteFiltration μ ℱ] {f : ι → Ω → ℝ} (
   rw [← neg_le_neg_iff, ← integral_neg, ← integral_neg]
   exact supermartingale.set_integral_le hf.neg hij hs
 #align measure_theory.submartingale.set_integral_le MeasureTheory.Submartingale.set_integral_le
+-/
 
+#print MeasureTheory.Submartingale.sub_supermartingale /-
 theorem sub_supermartingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)]
     (hf : Submartingale f ℱ μ) (hg : Supermartingale g ℱ μ) : Submartingale (f - g) ℱ μ := by
   rw [sub_eq_add_neg]; exact hf.add hg.neg
 #align measure_theory.submartingale.sub_supermartingale MeasureTheory.Submartingale.sub_supermartingale
+-/
 
+#print MeasureTheory.Submartingale.sub_martingale /-
 theorem sub_martingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Submartingale f ℱ μ)
     (hg : Martingale g ℱ μ) : Submartingale (f - g) ℱ μ :=
   hf.sub_supermartingale hg.Supermartingale
 #align measure_theory.submartingale.sub_martingale MeasureTheory.Submartingale.sub_martingale
+-/
 
+#print MeasureTheory.Submartingale.sup /-
 protected theorem sup {f g : ι → Ω → ℝ} (hf : Submartingale f ℱ μ) (hg : Submartingale g ℱ μ) :
     Submartingale (f ⊔ g) ℱ μ :=
   by
@@ -307,15 +382,19 @@ protected theorem sup {f g : ι → Ω → ℝ} (hf : Submartingale f ℱ μ) (h
         (condexp_mono (hg.integrable _) (integrable.sup (hf.integrable j) (hg.integrable j))
           (eventually_of_forall fun x => le_max_right _ _))
 #align measure_theory.submartingale.sup MeasureTheory.Submartingale.sup
+-/
 
+#print MeasureTheory.Submartingale.pos /-
 protected theorem pos {f : ι → Ω → ℝ} (hf : Submartingale f ℱ μ) : Submartingale (f⁺) ℱ μ :=
   hf.sup (martingale_zero _ _ _).Submartingale
 #align measure_theory.submartingale.pos MeasureTheory.Submartingale.pos
+-/
 
 end Submartingale
 
 section Submartingale
 
+#print MeasureTheory.submartingale_of_set_integral_le /-
 theorem submartingale_of_set_integral_le [IsFiniteMeasure μ] {f : ι → Ω → ℝ} (hadp : Adapted ℱ f)
     (hint : ∀ i, Integrable (f i) μ)
     (hf :
@@ -337,7 +416,9 @@ theorem submartingale_of_set_integral_le [IsFiniteMeasure μ] {f : ι → Ω →
     integral_sub' integrable_condexp.integrable_on (hint i).IntegrableOn, sub_nonneg,
     set_integral_condexp (ℱ.le i) (hint j) hs]
 #align measure_theory.submartingale_of_set_integral_le MeasureTheory.submartingale_of_set_integral_le
+-/
 
+#print MeasureTheory.submartingale_of_condexp_sub_nonneg /-
 theorem submartingale_of_condexp_sub_nonneg [IsFiniteMeasure μ] {f : ι → Ω → ℝ} (hadp : Adapted ℱ f)
     (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i j, i ≤ j → 0 ≤ᵐ[μ] μ[f j - f i|ℱ i]) :
     Submartingale f ℱ μ := by
@@ -346,7 +427,9 @@ theorem submartingale_of_condexp_sub_nonneg [IsFiniteMeasure μ] {f : ι → Ω
   exact eventually_le.trans (hf i j hij) (condexp_sub (hint _) (hint _)).le
   infer_instance
 #align measure_theory.submartingale_of_condexp_sub_nonneg MeasureTheory.submartingale_of_condexp_sub_nonneg
+-/
 
+#print MeasureTheory.Submartingale.condexp_sub_nonneg /-
 theorem Submartingale.condexp_sub_nonneg {f : ι → Ω → ℝ} (hf : Submartingale f ℱ μ) {i j : ι}
     (hij : i ≤ j) : 0 ≤ᵐ[μ] μ[f j - f i|ℱ i] :=
   by
@@ -358,33 +441,41 @@ theorem Submartingale.condexp_sub_nonneg {f : ι → Ω → ℝ} (hf : Submartin
   · exact hf.2.1 i j hij
   · exact h
 #align measure_theory.submartingale.condexp_sub_nonneg MeasureTheory.Submartingale.condexp_sub_nonneg
+-/
 
+#print MeasureTheory.submartingale_iff_condexp_sub_nonneg /-
 theorem submartingale_iff_condexp_sub_nonneg [IsFiniteMeasure μ] {f : ι → Ω → ℝ} :
     Submartingale f ℱ μ ↔
       Adapted ℱ f ∧ (∀ i, Integrable (f i) μ) ∧ ∀ i j, i ≤ j → 0 ≤ᵐ[μ] μ[f j - f i|ℱ i] :=
   ⟨fun h => ⟨h.Adapted, h.Integrable, fun i j => h.condexp_sub_nonneg⟩, fun ⟨hadp, hint, h⟩ =>
     submartingale_of_condexp_sub_nonneg hadp hint h⟩
 #align measure_theory.submartingale_iff_condexp_sub_nonneg MeasureTheory.submartingale_iff_condexp_sub_nonneg
+-/
 
 end Submartingale
 
 namespace Supermartingale
 
+#print MeasureTheory.Supermartingale.sub_submartingale /-
 theorem sub_submartingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)]
     (hf : Supermartingale f ℱ μ) (hg : Submartingale g ℱ μ) : Supermartingale (f - g) ℱ μ := by
   rw [sub_eq_add_neg]; exact hf.add hg.neg
 #align measure_theory.supermartingale.sub_submartingale MeasureTheory.Supermartingale.sub_submartingale
+-/
 
+#print MeasureTheory.Supermartingale.sub_martingale /-
 theorem sub_martingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)]
     (hf : Supermartingale f ℱ μ) (hg : Martingale g ℱ μ) : Supermartingale (f - g) ℱ μ :=
   hf.sub_submartingale hg.Submartingale
 #align measure_theory.supermartingale.sub_martingale MeasureTheory.Supermartingale.sub_martingale
+-/
 
 section
 
 variable {F : Type _} [NormedLatticeAddCommGroup F] [NormedSpace ℝ F] [CompleteSpace F]
   [OrderedSMul ℝ F]
 
+#print MeasureTheory.Supermartingale.smul_nonneg /-
 theorem smul_nonneg {f : ι → Ω → F} {c : ℝ} (hc : 0 ≤ c) (hf : Supermartingale f ℱ μ) :
     Supermartingale (c • f) ℱ μ :=
   by
@@ -394,13 +485,16 @@ theorem smul_nonneg {f : ι → Ω → F} {c : ℝ} (hc : 0 ≤ c) (hf : Superma
   simp_rw [Pi.smul_apply]
   exact smul_le_smul_of_nonneg hle hc
 #align measure_theory.supermartingale.smul_nonneg MeasureTheory.Supermartingale.smul_nonneg
+-/
 
+#print MeasureTheory.Supermartingale.smul_nonpos /-
 theorem smul_nonpos {f : ι → Ω → F} {c : ℝ} (hc : c ≤ 0) (hf : Supermartingale f ℱ μ) :
     Submartingale (c • f) ℱ μ :=
   by
   rw [← neg_neg c, (by ext (i x); simp : - -c • f = -(-c • f))]
   exact (hf.smul_nonneg <| neg_nonneg.2 hc).neg
 #align measure_theory.supermartingale.smul_nonpos MeasureTheory.Supermartingale.smul_nonpos
+-/
 
 end
 
@@ -413,19 +507,23 @@ section
 variable {F : Type _} [NormedLatticeAddCommGroup F] [NormedSpace ℝ F] [CompleteSpace F]
   [OrderedSMul ℝ F]
 
+#print MeasureTheory.Submartingale.smul_nonneg /-
 theorem smul_nonneg {f : ι → Ω → F} {c : ℝ} (hc : 0 ≤ c) (hf : Submartingale f ℱ μ) :
     Submartingale (c • f) ℱ μ :=
   by
   rw [← neg_neg c, (by ext (i x); simp : - -c • f = -(c • -f))]
   exact supermartingale.neg (hf.neg.smul_nonneg hc)
 #align measure_theory.submartingale.smul_nonneg MeasureTheory.Submartingale.smul_nonneg
+-/
 
+#print MeasureTheory.Submartingale.smul_nonpos /-
 theorem smul_nonpos {f : ι → Ω → F} {c : ℝ} (hc : c ≤ 0) (hf : Submartingale f ℱ μ) :
     Supermartingale (c • f) ℱ μ :=
   by
   rw [← neg_neg c, (by ext (i x); simp : - -c • f = -(-c • f))]
   exact (hf.smul_nonneg <| neg_nonneg.2 hc).neg
 #align measure_theory.submartingale.smul_nonpos MeasureTheory.Submartingale.smul_nonpos
+-/
 
 end
 
@@ -435,6 +533,7 @@ section Nat
 
 variable {𝒢 : Filtration ℕ m0}
 
+#print MeasureTheory.submartingale_of_set_integral_le_succ /-
 theorem submartingale_of_set_integral_le_succ [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
     (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
     (hf : ∀ i, ∀ s : Set Ω, measurable_set[𝒢 i] s → ∫ ω in s, f i ω ∂μ ≤ ∫ ω in s, f (i + 1) ω ∂μ) :
@@ -445,7 +544,9 @@ theorem submartingale_of_set_integral_le_succ [IsFiniteMeasure μ] {f : ℕ →
   · exact le_rfl
   · exact le_trans hk₂ (hf k s (𝒢.mono hk₁ _ hs))
 #align measure_theory.submartingale_of_set_integral_le_succ MeasureTheory.submartingale_of_set_integral_le_succ
+-/
 
+#print MeasureTheory.supermartingale_of_set_integral_succ_le /-
 theorem supermartingale_of_set_integral_succ_le [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
     (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
     (hf : ∀ i, ∀ s : Set Ω, measurable_set[𝒢 i] s → ∫ ω in s, f (i + 1) ω ∂μ ≤ ∫ ω in s, f i ω ∂μ) :
@@ -454,7 +555,9 @@ theorem supermartingale_of_set_integral_succ_le [IsFiniteMeasure μ] {f : ℕ 
   refine' (submartingale_of_set_integral_le_succ hadp.neg (fun i => (hint i).neg) _).neg
   simpa only [integral_neg, Pi.neg_apply, neg_le_neg_iff]
 #align measure_theory.supermartingale_of_set_integral_succ_le MeasureTheory.supermartingale_of_set_integral_succ_le
+-/
 
+#print MeasureTheory.martingale_of_set_integral_eq_succ /-
 theorem martingale_of_set_integral_eq_succ [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ)
     (hf : ∀ i, ∀ s : Set Ω, measurable_set[𝒢 i] s → ∫ ω in s, f i ω ∂μ = ∫ ω in s, f (i + 1) ω ∂μ) :
@@ -463,7 +566,9 @@ theorem martingale_of_set_integral_eq_succ [IsFiniteMeasure μ] {f : ℕ → Ω
     ⟨supermartingale_of_set_integral_succ_le hadp hint fun i s hs => (hf i s hs).ge,
       submartingale_of_set_integral_le_succ hadp hint fun i s hs => (hf i s hs).le⟩
 #align measure_theory.martingale_of_set_integral_eq_succ MeasureTheory.martingale_of_set_integral_eq_succ
+-/
 
+#print MeasureTheory.submartingale_nat /-
 theorem submartingale_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i, f i ≤ᵐ[μ] μ[f (i + 1)|𝒢 i]) : Submartingale f 𝒢 μ :=
   by
@@ -473,7 +578,9 @@ theorem submartingale_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp :
   rw [this]
   exact set_integral_mono_ae (hint i).IntegrableOn integrable_condexp.integrable_on (hf i)
 #align measure_theory.submartingale_nat MeasureTheory.submartingale_nat
+-/
 
+#print MeasureTheory.supermartingale_nat /-
 theorem supermartingale_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i, μ[f (i + 1)|𝒢 i] ≤ᵐ[μ] f i) :
     Supermartingale f 𝒢 μ := by
@@ -483,14 +590,18 @@ theorem supermartingale_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp
         eventually_le.trans _ (condexp_neg _).symm.le).neg
   filter_upwards [hf i] with x hx using neg_le_neg hx
 #align measure_theory.supermartingale_nat MeasureTheory.supermartingale_nat
+-/
 
+#print MeasureTheory.martingale_nat /-
 theorem martingale_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i, f i =ᵐ[μ] μ[f (i + 1)|𝒢 i]) : Martingale f 𝒢 μ :=
   martingale_iff.2
     ⟨supermartingale_nat hadp hint fun i => (hf i).symm.le,
       submartingale_nat hadp hint fun i => (hf i).le⟩
 #align measure_theory.martingale_nat MeasureTheory.martingale_nat
+-/
 
+#print MeasureTheory.submartingale_of_condexp_sub_nonneg_nat /-
 theorem submartingale_of_condexp_sub_nonneg_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
     (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
     (hf : ∀ i, 0 ≤ᵐ[μ] μ[f (i + 1) - f i|𝒢 i]) : Submartingale f 𝒢 μ :=
@@ -500,7 +611,9 @@ theorem submartingale_of_condexp_sub_nonneg_nat [IsFiniteMeasure μ] {f : ℕ 
   exact eventually_le.trans (hf i) (condexp_sub (hint _) (hint _)).le
   infer_instance
 #align measure_theory.submartingale_of_condexp_sub_nonneg_nat MeasureTheory.submartingale_of_condexp_sub_nonneg_nat
+-/
 
+#print MeasureTheory.supermartingale_of_condexp_sub_nonneg_nat /-
 theorem supermartingale_of_condexp_sub_nonneg_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
     (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
     (hf : ∀ i, 0 ≤ᵐ[μ] μ[f i - f (i + 1)|𝒢 i]) : Supermartingale f 𝒢 μ :=
@@ -509,7 +622,9 @@ theorem supermartingale_of_condexp_sub_nonneg_nat [IsFiniteMeasure μ] {f : ℕ
   refine' (submartingale_of_condexp_sub_nonneg_nat hadp.neg (fun i => (hint i).neg) _).neg
   simpa only [Pi.zero_apply, Pi.neg_apply, neg_sub_neg]
 #align measure_theory.supermartingale_of_condexp_sub_nonneg_nat MeasureTheory.supermartingale_of_condexp_sub_nonneg_nat
+-/
 
+#print MeasureTheory.martingale_of_condexp_sub_eq_zero_nat /-
 theorem martingale_of_condexp_sub_eq_zero_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
     (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
     (hf : ∀ i, μ[f (i + 1) - f i|𝒢 i] =ᵐ[μ] 0) : Martingale f 𝒢 μ :=
@@ -523,7 +638,9 @@ theorem martingale_of_condexp_sub_eq_zero_nat [IsFiniteMeasure μ] {f : ℕ →
   filter_upwards [hf i] with x hx
   simpa only [Pi.zero_apply, Pi.neg_apply, zero_eq_neg]
 #align measure_theory.martingale_of_condexp_sub_eq_zero_nat MeasureTheory.martingale_of_condexp_sub_eq_zero_nat
+-/
 
+#print MeasureTheory.Submartingale.zero_le_of_predictable /-
 -- Note that one cannot use `submartingale.zero_le_of_predictable` to prove the other two
 -- corresponding lemmas without imposing more restrictions to the ordering of `E`
 /-- A predictable submartingale is a.e. greater equal than its initial state. -/
@@ -540,7 +657,9 @@ theorem Submartingale.zero_le_of_predictable [Preorder E] [SigmaFiniteFiltration
             congr_arg coe <|
               condexp_of_strongly_measurable (𝒢.le _) (hfadp _) <| hfmgle.integrable _)
 #align measure_theory.submartingale.zero_le_of_predictable MeasureTheory.Submartingale.zero_le_of_predictable
+-/
 
+#print MeasureTheory.Supermartingale.le_zero_of_predictable /-
 /-- A predictable supermartingale is a.e. less equal than its initial state. -/
 theorem Supermartingale.le_zero_of_predictable [Preorder E] [SigmaFiniteFiltration μ 𝒢]
     {f : ℕ → Ω → E} (hfmgle : Supermartingale f 𝒢 μ) (hfadp : Adapted 𝒢 fun n => f (n + 1))
@@ -556,7 +675,9 @@ theorem Supermartingale.le_zero_of_predictable [Preorder E] [SigmaFiniteFiltrati
             (hfmgle.2.1 k (k + 1) k.le_succ)).trans
         ih
 #align measure_theory.supermartingale.le_zero_of_predictable MeasureTheory.Supermartingale.le_zero_of_predictable
+-/
 
+#print MeasureTheory.Martingale.eq_zero_of_predictable /-
 /-- A predictable martingale is a.e. equal to its initial state. -/
 theorem Martingale.eq_zero_of_predictable [SigmaFiniteFiltration μ 𝒢] {f : ℕ → Ω → E}
     (hfmgle : Martingale f 𝒢 μ) (hfadp : Adapted 𝒢 fun n => f (n + 1)) (n : ℕ) : f n =ᵐ[μ] f 0 :=
@@ -572,17 +693,21 @@ theorem Martingale.eq_zero_of_predictable [SigmaFiniteFiltration μ 𝒢] {f : 
             (hfmgle.2 k (k + 1) k.le_succ)).trans
         ih
 #align measure_theory.martingale.eq_zero_of_predictable MeasureTheory.Martingale.eq_zero_of_predictable
+-/
 
 namespace Submartingale
 
+#print MeasureTheory.Submartingale.integrable_stoppedValue /-
 @[protected]
 theorem integrable_stoppedValue [LE E] {f : ℕ → Ω → E} (hf : Submartingale f 𝒢 μ) {τ : Ω → ℕ}
     (hτ : IsStoppingTime 𝒢 τ) {N : ℕ} (hbdd : ∀ ω, τ ω ≤ N) : Integrable (stoppedValue f τ) μ :=
   integrable_stoppedValue ℕ hτ hf.Integrable hbdd
 #align measure_theory.submartingale.integrable_stopped_value MeasureTheory.Submartingale.integrable_stoppedValue
+-/
 
 end Submartingale
 
+#print MeasureTheory.Submartingale.sum_mul_sub /-
 theorem Submartingale.sum_mul_sub [IsFiniteMeasure μ] {R : ℝ} {ξ f : ℕ → Ω → ℝ}
     (hf : Submartingale f 𝒢 μ) (hξ : Adapted 𝒢 ξ) (hbdd : ∀ n ω, ξ n ω ≤ R)
     (hnonneg : ∀ n ω, 0 ≤ ξ n ω) :
@@ -615,7 +740,9 @@ theorem Submartingale.sum_mul_sub [IsFiniteMeasure μ] {R : ℝ} {ξ f : ℕ →
               hξ.strongly_measurable.ae_strongly_measurable (hξbdd _))
             ((hf.integrable _).sub (hf.integrable _))).symm.le
 #align measure_theory.submartingale.sum_mul_sub MeasureTheory.Submartingale.sum_mul_sub
+-/
 
+#print MeasureTheory.Submartingale.sum_mul_sub' /-
 /-- Given a discrete submartingale `f` and a predictable process `ξ` (i.e. `ξ (n + 1)` is adapted)
 the process defined by `λ n, ∑ k in finset.range n, ξ (k + 1) * (f (k + 1) - f k)` is also a
 submartingale. -/
@@ -625,6 +752,7 @@ theorem Submartingale.sum_mul_sub' [IsFiniteMeasure μ] {R : ℝ} {ξ f : ℕ 
     Submartingale (fun n => ∑ k in Finset.range n, ξ (k + 1) * (f (k + 1) - f k)) 𝒢 μ :=
   hf.sum_mul_sub hξ (fun n => hbdd _) fun n => hnonneg _
 #align measure_theory.submartingale.sum_mul_sub' MeasureTheory.Submartingale.sum_mul_sub'
+-/
 
 end Nat
 

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

@@ -117,7 +117,7 @@ theorem integrable (hf : Martingale f ℱ μ) (i : ι) : Integrable (f i) μ :=
 #align measure_theory.martingale.integrable MeasureTheory.Martingale.integrable
 
 theorem set_integral_eq [SigmaFiniteFiltration μ ℱ] (hf : Martingale f ℱ μ) {i j : ι} (hij : i ≤ j)
-    {s : Set Ω} (hs : measurable_set[ℱ i] s) : (∫ ω in s, f i ω ∂μ) = ∫ ω in s, f j ω ∂μ :=
+    {s : Set Ω} (hs : measurable_set[ℱ i] s) : ∫ ω in s, f i ω ∂μ = ∫ ω in s, f j ω ∂μ :=
   by
   rw [← @set_integral_condexp _ _ _ _ _ (ℱ i) m0 _ _ _ (ℱ.le i) _ (hf.integrable j) hs]
   refine' set_integral_congr_ae (ℱ.le i s hs) _
@@ -191,7 +191,7 @@ theorem condexp_ae_le [LE E] (hf : Supermartingale f ℱ μ) {i j : ι} (hij : i
 
 theorem set_integral_le [SigmaFiniteFiltration μ ℱ] {f : ι → Ω → ℝ} (hf : Supermartingale f ℱ μ)
     {i j : ι} (hij : i ≤ j) {s : Set Ω} (hs : measurable_set[ℱ i] s) :
-    (∫ ω in s, f j ω ∂μ) ≤ ∫ ω in s, f i ω ∂μ :=
+    ∫ ω in s, f j ω ∂μ ≤ ∫ ω in s, f i ω ∂μ :=
   by
   rw [← set_integral_condexp (ℱ.le i) (hf.integrable j) hs]
   refine' set_integral_mono_ae integrable_condexp.integrable_on (hf.integrable i).IntegrableOn _
@@ -273,7 +273,7 @@ theorem neg [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Submar
 /-- The converse of this lemma is `measure_theory.submartingale_of_set_integral_le`. -/
 theorem set_integral_le [SigmaFiniteFiltration μ ℱ] {f : ι → Ω → ℝ} (hf : Submartingale f ℱ μ)
     {i j : ι} (hij : i ≤ j) {s : Set Ω} (hs : measurable_set[ℱ i] s) :
-    (∫ ω in s, f i ω ∂μ) ≤ ∫ ω in s, f j ω ∂μ :=
+    ∫ ω in s, f i ω ∂μ ≤ ∫ ω in s, f j ω ∂μ :=
   by
   rw [← neg_le_neg_iff, ← integral_neg, ← integral_neg]
   exact supermartingale.set_integral_le hf.neg hij hs
@@ -320,7 +320,7 @@ theorem submartingale_of_set_integral_le [IsFiniteMeasure μ] {f : ι → Ω →
     (hint : ∀ i, Integrable (f i) μ)
     (hf :
       ∀ i j : ι,
-        i ≤ j → ∀ s : Set Ω, measurable_set[ℱ i] s → (∫ ω in s, f i ω ∂μ) ≤ ∫ ω in s, f j ω ∂μ) :
+        i ≤ j → ∀ s : Set Ω, measurable_set[ℱ i] s → ∫ ω in s, f i ω ∂μ ≤ ∫ ω in s, f j ω ∂μ) :
     Submartingale f ℱ μ := by
   refine' ⟨hadp, fun i j hij => _, hint⟩
   suffices f i ≤ᵐ[μ.trim (ℱ.le i)] μ[f j|ℱ i] by exact ae_le_of_ae_le_trim this
@@ -437,8 +437,7 @@ variable {𝒢 : Filtration ℕ m0}
 
 theorem submartingale_of_set_integral_le_succ [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
     (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
-    (hf :
-      ∀ i, ∀ s : Set Ω, measurable_set[𝒢 i] s → (∫ ω in s, f i ω ∂μ) ≤ ∫ ω in s, f (i + 1) ω ∂μ) :
+    (hf : ∀ i, ∀ s : Set Ω, measurable_set[𝒢 i] s → ∫ ω in s, f i ω ∂μ ≤ ∫ ω in s, f (i + 1) ω ∂μ) :
     Submartingale f 𝒢 μ :=
   by
   refine' submartingale_of_set_integral_le hadp hint fun i j hij s hs => _
@@ -449,8 +448,7 @@ theorem submartingale_of_set_integral_le_succ [IsFiniteMeasure μ] {f : ℕ →
 
 theorem supermartingale_of_set_integral_succ_le [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
     (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
-    (hf :
-      ∀ i, ∀ s : Set Ω, measurable_set[𝒢 i] s → (∫ ω in s, f (i + 1) ω ∂μ) ≤ ∫ ω in s, f i ω ∂μ) :
+    (hf : ∀ i, ∀ s : Set Ω, measurable_set[𝒢 i] s → ∫ ω in s, f (i + 1) ω ∂μ ≤ ∫ ω in s, f i ω ∂μ) :
     Supermartingale f 𝒢 μ := by
   rw [← neg_neg f]
   refine' (submartingale_of_set_integral_le_succ hadp.neg (fun i => (hint i).neg) _).neg
@@ -459,8 +457,7 @@ theorem supermartingale_of_set_integral_succ_le [IsFiniteMeasure μ] {f : ℕ 
 
 theorem martingale_of_set_integral_eq_succ [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ)
-    (hf :
-      ∀ i, ∀ s : Set Ω, measurable_set[𝒢 i] s → (∫ ω in s, f i ω ∂μ) = ∫ ω in s, f (i + 1) ω ∂μ) :
+    (hf : ∀ i, ∀ s : Set Ω, measurable_set[𝒢 i] s → ∫ ω in s, f i ω ∂μ = ∫ ω in s, f (i + 1) ω ∂μ) :
     Martingale f 𝒢 μ :=
   martingale_iff.2
     ⟨supermartingale_of_set_integral_succ_le hadp hint fun i s hs => (hf i s hs).ge,
@@ -471,7 +468,7 @@ theorem submartingale_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp :
     (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i, f i ≤ᵐ[μ] μ[f (i + 1)|𝒢 i]) : Submartingale f 𝒢 μ :=
   by
   refine' submartingale_of_set_integral_le_succ hadp hint fun i s hs => _
-  have : (∫ ω in s, f (i + 1) ω ∂μ) = ∫ ω in s, (μ[f (i + 1)|𝒢 i]) ω ∂μ :=
+  have : ∫ ω in s, f (i + 1) ω ∂μ = ∫ ω in s, (μ[f (i + 1)|𝒢 i]) ω ∂μ :=
     (set_integral_condexp (𝒢.le i) (hint _) hs).symm
   rw [this]
   exact set_integral_mono_ae (hint i).IntegrableOn integrable_condexp.integrable_on (hf i)

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne, Kexing Ying
 
 ! This file was ported from Lean 3 source module probability.martingale.basic
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit ba074af83b6cf54c3104e59402b39410ddbd6dca
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -391,7 +391,7 @@ theorem smul_nonneg {f : ι → Ω → F} {c : ℝ} (hc : 0 ≤ c) (hf : Superma
   refine' ⟨hf.1.smul c, fun i j hij => _, fun i => (hf.2.2 i).smul c⟩
   refine' (condexp_smul c (f j)).le.trans _
   filter_upwards [hf.2.1 i j hij] with _ hle
-  simp
+  simp_rw [Pi.smul_apply]
   exact smul_le_smul_of_nonneg hle hc
 #align measure_theory.supermartingale.smul_nonneg MeasureTheory.Supermartingale.smul_nonneg
 

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

@@ -73,12 +73,12 @@ def Submartingale [LE E] (f : ι → Ω → E) (ℱ : Filtration ι m0)
   Adapted ℱ f ∧ (∀ i j, i ≤ j → f i ≤ᵐ[μ] μ[f j|ℱ i]) ∧ ∀ i, Integrable (f i) μ
 #align measure_theory.submartingale MeasureTheory.Submartingale
 
-theorem martingale_const (ℱ : Filtration ι m0) (μ : Measure Ω) [FiniteMeasure μ] (x : E) :
+theorem martingale_const (ℱ : Filtration ι m0) (μ : Measure Ω) [IsFiniteMeasure μ] (x : E) :
     Martingale (fun _ _ => x) ℱ μ :=
   ⟨adapted_const ℱ _, fun i j hij => by rw [condexp_const (ℱ.le _)]⟩
 #align measure_theory.martingale_const MeasureTheory.martingale_const
 
-theorem martingale_const_fun [OrderBot ι] (ℱ : Filtration ι m0) (μ : Measure Ω) [FiniteMeasure μ]
+theorem martingale_const_fun [OrderBot ι] (ℱ : Filtration ι m0) (μ : Measure Ω) [IsFiniteMeasure μ]
     {f : Ω → E} (hf : strongly_measurable[ℱ ⊥] f) (hfint : Integrable f μ) :
     Martingale (fun _ => f) ℱ μ :=
   by
@@ -121,7 +121,7 @@ theorem set_integral_eq [SigmaFiniteFiltration μ ℱ] (hf : Martingale f ℱ μ
   by
   rw [← @set_integral_condexp _ _ _ _ _ (ℱ i) m0 _ _ _ (ℱ.le i) _ (hf.integrable j) hs]
   refine' set_integral_congr_ae (ℱ.le i s hs) _
-  filter_upwards [hf.2 i j hij]with _ heq _ using HEq.symm
+  filter_upwards [hf.2 i j hij] with _ heq _ using HEq.symm
 #align measure_theory.martingale.set_integral_eq MeasureTheory.Martingale.set_integral_eq
 
 theorem add (hf : Martingale f ℱ μ) (hg : Martingale g ℱ μ) : Martingale (f + g) ℱ μ :=
@@ -195,7 +195,7 @@ theorem set_integral_le [SigmaFiniteFiltration μ ℱ] {f : ι → Ω → ℝ} (
   by
   rw [← set_integral_condexp (ℱ.le i) (hf.integrable j) hs]
   refine' set_integral_mono_ae integrable_condexp.integrable_on (hf.integrable i).IntegrableOn _
-  filter_upwards [hf.2.1 i j hij]with _ heq using HEq
+  filter_upwards [hf.2.1 i j hij] with _ heq using HEq
 #align measure_theory.supermartingale.set_integral_le MeasureTheory.Supermartingale.set_integral_le
 
 theorem add [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Supermartingale f ℱ μ)
@@ -218,7 +218,7 @@ theorem neg [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Superm
   by
   refine' ⟨hf.1.neg, fun i j hij => _, fun i => (hf.2.2 i).neg⟩
   refine' eventually_le.trans _ (condexp_neg (f j)).symm.le
-  filter_upwards [hf.2.1 i j hij]with _ _
+  filter_upwards [hf.2.1 i j hij] with _ _
   simpa
 #align measure_theory.supermartingale.neg MeasureTheory.Supermartingale.neg
 
@@ -266,7 +266,7 @@ theorem neg [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Submar
     Supermartingale (-f) ℱ μ :=
   by
   refine' ⟨hf.1.neg, fun i j hij => (condexp_neg (f j)).le.trans _, fun i => (hf.2.2 i).neg⟩
-  filter_upwards [hf.2.1 i j hij]with _ _
+  filter_upwards [hf.2.1 i j hij] with _ _
   simpa
 #align measure_theory.submartingale.neg MeasureTheory.Submartingale.neg
 
@@ -316,7 +316,7 @@ end Submartingale
 
 section Submartingale
 
-theorem submartingale_of_set_integral_le [FiniteMeasure μ] {f : ι → Ω → ℝ} (hadp : Adapted ℱ f)
+theorem submartingale_of_set_integral_le [IsFiniteMeasure μ] {f : ι → Ω → ℝ} (hadp : Adapted ℱ f)
     (hint : ∀ i, Integrable (f i) μ)
     (hf :
       ∀ i j : ι,
@@ -326,7 +326,7 @@ theorem submartingale_of_set_integral_le [FiniteMeasure μ] {f : ι → Ω → 
   suffices f i ≤ᵐ[μ.trim (ℱ.le i)] μ[f j|ℱ i] by exact ae_le_of_ae_le_trim this
   suffices 0 ≤ᵐ[μ.trim (ℱ.le i)] μ[f j|ℱ i] - f i
     by
-    filter_upwards [this]with x hx
+    filter_upwards [this] with x hx
     rwa [← sub_nonneg]
   refine'
     ae_nonneg_of_forall_set_integral_nonneg
@@ -338,7 +338,7 @@ theorem submartingale_of_set_integral_le [FiniteMeasure μ] {f : ι → Ω → 
     set_integral_condexp (ℱ.le i) (hint j) hs]
 #align measure_theory.submartingale_of_set_integral_le MeasureTheory.submartingale_of_set_integral_le
 
-theorem submartingale_of_condexp_sub_nonneg [FiniteMeasure μ] {f : ι → Ω → ℝ} (hadp : Adapted ℱ f)
+theorem submartingale_of_condexp_sub_nonneg [IsFiniteMeasure μ] {f : ι → Ω → ℝ} (hadp : Adapted ℱ f)
     (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i j, i ≤ j → 0 ≤ᵐ[μ] μ[f j - f i|ℱ i]) :
     Submartingale f ℱ μ := by
   refine' ⟨hadp, fun i j hij => _, hint⟩
@@ -359,7 +359,7 @@ theorem Submartingale.condexp_sub_nonneg {f : ι → Ω → ℝ} (hf : Submartin
   · exact h
 #align measure_theory.submartingale.condexp_sub_nonneg MeasureTheory.Submartingale.condexp_sub_nonneg
 
-theorem submartingale_iff_condexp_sub_nonneg [FiniteMeasure μ] {f : ι → Ω → ℝ} :
+theorem submartingale_iff_condexp_sub_nonneg [IsFiniteMeasure μ] {f : ι → Ω → ℝ} :
     Submartingale f ℱ μ ↔
       Adapted ℱ f ∧ (∀ i, Integrable (f i) μ) ∧ ∀ i j, i ≤ j → 0 ≤ᵐ[μ] μ[f j - f i|ℱ i] :=
   ⟨fun h => ⟨h.Adapted, h.Integrable, fun i j => h.condexp_sub_nonneg⟩, fun ⟨hadp, hint, h⟩ =>
@@ -390,7 +390,7 @@ theorem smul_nonneg {f : ι → Ω → F} {c : ℝ} (hc : 0 ≤ c) (hf : Superma
   by
   refine' ⟨hf.1.smul c, fun i j hij => _, fun i => (hf.2.2 i).smul c⟩
   refine' (condexp_smul c (f j)).le.trans _
-  filter_upwards [hf.2.1 i j hij]with _ hle
+  filter_upwards [hf.2.1 i j hij] with _ hle
   simp
   exact smul_le_smul_of_nonneg hle hc
 #align measure_theory.supermartingale.smul_nonneg MeasureTheory.Supermartingale.smul_nonneg
@@ -435,8 +435,8 @@ section Nat
 
 variable {𝒢 : Filtration ℕ m0}
 
-theorem submartingale_of_set_integral_le_succ [FiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
-    (hint : ∀ i, Integrable (f i) μ)
+theorem submartingale_of_set_integral_le_succ [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
+    (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
     (hf :
       ∀ i, ∀ s : Set Ω, measurable_set[𝒢 i] s → (∫ ω in s, f i ω ∂μ) ≤ ∫ ω in s, f (i + 1) ω ∂μ) :
     Submartingale f 𝒢 μ :=
@@ -447,7 +447,7 @@ theorem submartingale_of_set_integral_le_succ [FiniteMeasure μ] {f : ℕ → Ω
   · exact le_trans hk₂ (hf k s (𝒢.mono hk₁ _ hs))
 #align measure_theory.submartingale_of_set_integral_le_succ MeasureTheory.submartingale_of_set_integral_le_succ
 
-theorem supermartingale_of_set_integral_succ_le [FiniteMeasure μ] {f : ℕ → Ω → ℝ}
+theorem supermartingale_of_set_integral_succ_le [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
     (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
     (hf :
       ∀ i, ∀ s : Set Ω, measurable_set[𝒢 i] s → (∫ ω in s, f (i + 1) ω ∂μ) ≤ ∫ ω in s, f i ω ∂μ) :
@@ -457,7 +457,7 @@ theorem supermartingale_of_set_integral_succ_le [FiniteMeasure μ] {f : ℕ →
   simpa only [integral_neg, Pi.neg_apply, neg_le_neg_iff]
 #align measure_theory.supermartingale_of_set_integral_succ_le MeasureTheory.supermartingale_of_set_integral_succ_le
 
-theorem martingale_of_set_integral_eq_succ [FiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
+theorem martingale_of_set_integral_eq_succ [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ)
     (hf :
       ∀ i, ∀ s : Set Ω, measurable_set[𝒢 i] s → (∫ ω in s, f i ω ∂μ) = ∫ ω in s, f (i + 1) ω ∂μ) :
@@ -467,7 +467,7 @@ theorem martingale_of_set_integral_eq_succ [FiniteMeasure μ] {f : ℕ → Ω 
       submartingale_of_set_integral_le_succ hadp hint fun i s hs => (hf i s hs).le⟩
 #align measure_theory.martingale_of_set_integral_eq_succ MeasureTheory.martingale_of_set_integral_eq_succ
 
-theorem submartingale_nat [FiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
+theorem submartingale_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i, f i ≤ᵐ[μ] μ[f (i + 1)|𝒢 i]) : Submartingale f 𝒢 μ :=
   by
   refine' submartingale_of_set_integral_le_succ hadp hint fun i s hs => _
@@ -477,24 +477,24 @@ theorem submartingale_nat [FiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Ad
   exact set_integral_mono_ae (hint i).IntegrableOn integrable_condexp.integrable_on (hf i)
 #align measure_theory.submartingale_nat MeasureTheory.submartingale_nat
 
-theorem supermartingale_nat [FiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
+theorem supermartingale_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i, μ[f (i + 1)|𝒢 i] ≤ᵐ[μ] f i) :
     Supermartingale f 𝒢 μ := by
   rw [← neg_neg f]
   refine'
     (submartingale_nat hadp.neg (fun i => (hint i).neg) fun i =>
         eventually_le.trans _ (condexp_neg _).symm.le).neg
-  filter_upwards [hf i]with x hx using neg_le_neg hx
+  filter_upwards [hf i] with x hx using neg_le_neg hx
 #align measure_theory.supermartingale_nat MeasureTheory.supermartingale_nat
 
-theorem martingale_nat [FiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
+theorem martingale_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i, f i =ᵐ[μ] μ[f (i + 1)|𝒢 i]) : Martingale f 𝒢 μ :=
   martingale_iff.2
     ⟨supermartingale_nat hadp hint fun i => (hf i).symm.le,
       submartingale_nat hadp hint fun i => (hf i).le⟩
 #align measure_theory.martingale_nat MeasureTheory.martingale_nat
 
-theorem submartingale_of_condexp_sub_nonneg_nat [FiniteMeasure μ] {f : ℕ → Ω → ℝ}
+theorem submartingale_of_condexp_sub_nonneg_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
     (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
     (hf : ∀ i, 0 ≤ᵐ[μ] μ[f (i + 1) - f i|𝒢 i]) : Submartingale f 𝒢 μ :=
   by
@@ -504,7 +504,7 @@ theorem submartingale_of_condexp_sub_nonneg_nat [FiniteMeasure μ] {f : ℕ →
   infer_instance
 #align measure_theory.submartingale_of_condexp_sub_nonneg_nat MeasureTheory.submartingale_of_condexp_sub_nonneg_nat
 
-theorem supermartingale_of_condexp_sub_nonneg_nat [FiniteMeasure μ] {f : ℕ → Ω → ℝ}
+theorem supermartingale_of_condexp_sub_nonneg_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
     (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
     (hf : ∀ i, 0 ≤ᵐ[μ] μ[f i - f (i + 1)|𝒢 i]) : Supermartingale f 𝒢 μ :=
   by
@@ -513,9 +513,9 @@ theorem supermartingale_of_condexp_sub_nonneg_nat [FiniteMeasure μ] {f : ℕ 
   simpa only [Pi.zero_apply, Pi.neg_apply, neg_sub_neg]
 #align measure_theory.supermartingale_of_condexp_sub_nonneg_nat MeasureTheory.supermartingale_of_condexp_sub_nonneg_nat
 
-theorem martingale_of_condexp_sub_eq_zero_nat [FiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
-    (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i, μ[f (i + 1) - f i|𝒢 i] =ᵐ[μ] 0) :
-    Martingale f 𝒢 μ :=
+theorem martingale_of_condexp_sub_eq_zero_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
+    (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
+    (hf : ∀ i, μ[f (i + 1) - f i|𝒢 i] =ᵐ[μ] 0) : Martingale f 𝒢 μ :=
   by
   refine'
     martingale_iff.2
@@ -523,7 +523,7 @@ theorem martingale_of_condexp_sub_eq_zero_nat [FiniteMeasure μ] {f : ℕ → Ω
         submartingale_of_condexp_sub_nonneg_nat hadp hint fun i => (hf i).symm.le⟩
   rw [← neg_sub]
   refine' (eventually_eq.trans _ (condexp_neg _).symm).le
-  filter_upwards [hf i]with x hx
+  filter_upwards [hf i] with x hx
   simpa only [Pi.zero_apply, Pi.neg_apply, zero_eq_neg]
 #align measure_theory.martingale_of_condexp_sub_eq_zero_nat MeasureTheory.martingale_of_condexp_sub_eq_zero_nat
 
@@ -586,7 +586,7 @@ theorem integrable_stoppedValue [LE E] {f : ℕ → Ω → E} (hf : Submartingal
 
 end Submartingale
 
-theorem Submartingale.sum_mul_sub [FiniteMeasure μ] {R : ℝ} {ξ f : ℕ → Ω → ℝ}
+theorem Submartingale.sum_mul_sub [IsFiniteMeasure μ] {R : ℝ} {ξ f : ℕ → Ω → ℝ}
     (hf : Submartingale f 𝒢 μ) (hξ : Adapted 𝒢 ξ) (hbdd : ∀ n ω, ξ n ω ≤ R)
     (hnonneg : ∀ n ω, 0 ≤ ξ n ω) :
     Submartingale (fun n => ∑ k in Finset.range n, ξ k * (f (k + 1) - f k)) 𝒢 μ :=
@@ -622,7 +622,7 @@ theorem Submartingale.sum_mul_sub [FiniteMeasure μ] {R : ℝ} {ξ f : ℕ → 
 /-- Given a discrete submartingale `f` and a predictable process `ξ` (i.e. `ξ (n + 1)` is adapted)
 the process defined by `λ n, ∑ k in finset.range n, ξ (k + 1) * (f (k + 1) - f k)` is also a
 submartingale. -/
-theorem Submartingale.sum_mul_sub' [FiniteMeasure μ] {R : ℝ} {ξ f : ℕ → Ω → ℝ}
+theorem Submartingale.sum_mul_sub' [IsFiniteMeasure μ] {R : ℝ} {ξ f : ℕ → Ω → ℝ}
     (hf : Submartingale f 𝒢 μ) (hξ : Adapted 𝒢 fun n => ξ (n + 1)) (hbdd : ∀ n ω, ξ n ω ≤ R)
     (hnonneg : ∀ n ω, 0 ≤ ξ n ω) :
     Submartingale (fun n => ∑ k in Finset.range n, ξ (k + 1) * (f (k + 1) - f k)) 𝒢 μ :=

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

@@ -601,7 +601,7 @@ theorem Submartingale.sum_mul_sub [FiniteMeasure μ] {R : ℝ} {ξ f : ℕ → 
     by
     intro m
     refine' Finset.stronglyMeasurable_sum' _ fun i hi => _
-    rw [Finset.mem_range] at hi
+    rw [Finset.mem_range] at hi 
     exact
       (hξ.strongly_measurable_le hi.le).mul
         ((hf.adapted.strongly_measurable_le (Nat.succ_le_of_lt hi)).sub

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

@@ -43,7 +43,7 @@ The definitions of filtration and adapted can be found in `probability.stopping`
 
 open TopologicalSpace Filter
 
-open NNReal ENNReal MeasureTheory ProbabilityTheory BigOperators
+open scoped NNReal ENNReal MeasureTheory ProbabilityTheory BigOperators
 
 namespace MeasureTheory
 

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

@@ -90,10 +90,7 @@ theorem martingale_const_fun [OrderBot ι] (ℱ : Filtration ι m0) (μ : Measur
 variable (E)
 
 theorem martingale_zero (ℱ : Filtration ι m0) (μ : Measure Ω) : Martingale (0 : ι → Ω → E) ℱ μ :=
-  ⟨adapted_zero E ℱ, fun i j hij =>
-    by
-    rw [Pi.zero_apply, condexp_zero]
-    simp⟩
+  ⟨adapted_zero E ℱ, fun i j hij => by rw [Pi.zero_apply, condexp_zero]; simp⟩
 #align measure_theory.martingale_zero MeasureTheory.martingale_zero
 
 variable {E}
@@ -137,10 +134,8 @@ theorem neg (hf : Martingale f ℱ μ) : Martingale (-f) ℱ μ :=
   ⟨hf.Adapted.neg, fun i j hij => (condexp_neg (f j)).trans (hf.2 i j hij).neg⟩
 #align measure_theory.martingale.neg MeasureTheory.Martingale.neg
 
-theorem sub (hf : Martingale f ℱ μ) (hg : Martingale g ℱ μ) : Martingale (f - g) ℱ μ :=
-  by
-  rw [sub_eq_add_neg]
-  exact hf.add hg.neg
+theorem sub (hf : Martingale f ℱ μ) (hg : Martingale g ℱ μ) : Martingale (f - g) ℱ μ := by
+  rw [sub_eq_add_neg]; exact hf.add hg.neg
 #align measure_theory.martingale.sub MeasureTheory.Martingale.sub
 
 theorem smul (c : ℝ) (hf : Martingale f ℱ μ) : Martingale (c • f) ℱ μ :=
@@ -285,10 +280,8 @@ theorem set_integral_le [SigmaFiniteFiltration μ ℱ] {f : ι → Ω → ℝ} (
 #align measure_theory.submartingale.set_integral_le MeasureTheory.Submartingale.set_integral_le
 
 theorem sub_supermartingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)]
-    (hf : Submartingale f ℱ μ) (hg : Supermartingale g ℱ μ) : Submartingale (f - g) ℱ μ :=
-  by
-  rw [sub_eq_add_neg]
-  exact hf.add hg.neg
+    (hf : Submartingale f ℱ μ) (hg : Supermartingale g ℱ μ) : Submartingale (f - g) ℱ μ := by
+  rw [sub_eq_add_neg]; exact hf.add hg.neg
 #align measure_theory.submartingale.sub_supermartingale MeasureTheory.Submartingale.sub_supermartingale
 
 theorem sub_martingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Submartingale f ℱ μ)
@@ -378,10 +371,8 @@ end Submartingale
 namespace Supermartingale
 
 theorem sub_submartingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)]
-    (hf : Supermartingale f ℱ μ) (hg : Submartingale g ℱ μ) : Supermartingale (f - g) ℱ μ :=
-  by
-  rw [sub_eq_add_neg]
-  exact hf.add hg.neg
+    (hf : Supermartingale f ℱ μ) (hg : Submartingale g ℱ μ) : Supermartingale (f - g) ℱ μ := by
+  rw [sub_eq_add_neg]; exact hf.add hg.neg
 #align measure_theory.supermartingale.sub_submartingale MeasureTheory.Supermartingale.sub_submartingale
 
 theorem sub_martingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)]
@@ -407,10 +398,7 @@ theorem smul_nonneg {f : ι → Ω → F} {c : ℝ} (hc : 0 ≤ c) (hf : Superma
 theorem smul_nonpos {f : ι → Ω → F} {c : ℝ} (hc : c ≤ 0) (hf : Supermartingale f ℱ μ) :
     Submartingale (c • f) ℱ μ :=
   by
-  rw [← neg_neg c,
-    (by
-      ext (i x)
-      simp : - -c • f = -(-c • f))]
+  rw [← neg_neg c, (by ext (i x); simp : - -c • f = -(-c • f))]
   exact (hf.smul_nonneg <| neg_nonneg.2 hc).neg
 #align measure_theory.supermartingale.smul_nonpos MeasureTheory.Supermartingale.smul_nonpos
 
@@ -428,20 +416,14 @@ variable {F : Type _} [NormedLatticeAddCommGroup F] [NormedSpace ℝ F] [Complet
 theorem smul_nonneg {f : ι → Ω → F} {c : ℝ} (hc : 0 ≤ c) (hf : Submartingale f ℱ μ) :
     Submartingale (c • f) ℱ μ :=
   by
-  rw [← neg_neg c,
-    (by
-      ext (i x)
-      simp : - -c • f = -(c • -f))]
+  rw [← neg_neg c, (by ext (i x); simp : - -c • f = -(c • -f))]
   exact supermartingale.neg (hf.neg.smul_nonneg hc)
 #align measure_theory.submartingale.smul_nonneg MeasureTheory.Submartingale.smul_nonneg
 
 theorem smul_nonpos {f : ι → Ω → F} {c : ℝ} (hc : c ≤ 0) (hf : Submartingale f ℱ μ) :
     Supermartingale (c • f) ℱ μ :=
   by
-  rw [← neg_neg c,
-    (by
-      ext (i x)
-      simp : - -c • f = -(-c • f))]
+  rw [← neg_neg c, (by ext (i x); simp : - -c • f = -(-c • f))]
   exact (hf.smul_nonneg <| neg_nonneg.2 hc).neg
 #align measure_theory.submartingale.smul_nonpos MeasureTheory.Submartingale.smul_nonpos
 

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

@@ -73,12 +73,12 @@ def Submartingale [LE E] (f : ι → Ω → E) (ℱ : Filtration ι m0)
   Adapted ℱ f ∧ (∀ i j, i ≤ j → f i ≤ᵐ[μ] μ[f j|ℱ i]) ∧ ∀ i, Integrable (f i) μ
 #align measure_theory.submartingale MeasureTheory.Submartingale
 
-theorem martingale_const (ℱ : Filtration ι m0) (μ : Measure Ω) [IsFiniteMeasure μ] (x : E) :
+theorem martingale_const (ℱ : Filtration ι m0) (μ : Measure Ω) [FiniteMeasure μ] (x : E) :
     Martingale (fun _ _ => x) ℱ μ :=
   ⟨adapted_const ℱ _, fun i j hij => by rw [condexp_const (ℱ.le _)]⟩
 #align measure_theory.martingale_const MeasureTheory.martingale_const
 
-theorem martingale_const_fun [OrderBot ι] (ℱ : Filtration ι m0) (μ : Measure Ω) [IsFiniteMeasure μ]
+theorem martingale_const_fun [OrderBot ι] (ℱ : Filtration ι m0) (μ : Measure Ω) [FiniteMeasure μ]
     {f : Ω → E} (hf : strongly_measurable[ℱ ⊥] f) (hfint : Integrable f μ) :
     Martingale (fun _ => f) ℱ μ :=
   by
@@ -323,7 +323,7 @@ end Submartingale
 
 section Submartingale
 
-theorem submartingale_of_set_integral_le [IsFiniteMeasure μ] {f : ι → Ω → ℝ} (hadp : Adapted ℱ f)
+theorem submartingale_of_set_integral_le [FiniteMeasure μ] {f : ι → Ω → ℝ} (hadp : Adapted ℱ f)
     (hint : ∀ i, Integrable (f i) μ)
     (hf :
       ∀ i j : ι,
@@ -345,7 +345,7 @@ theorem submartingale_of_set_integral_le [IsFiniteMeasure μ] {f : ι → Ω →
     set_integral_condexp (ℱ.le i) (hint j) hs]
 #align measure_theory.submartingale_of_set_integral_le MeasureTheory.submartingale_of_set_integral_le
 
-theorem submartingale_of_condexp_sub_nonneg [IsFiniteMeasure μ] {f : ι → Ω → ℝ} (hadp : Adapted ℱ f)
+theorem submartingale_of_condexp_sub_nonneg [FiniteMeasure μ] {f : ι → Ω → ℝ} (hadp : Adapted ℱ f)
     (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i j, i ≤ j → 0 ≤ᵐ[μ] μ[f j - f i|ℱ i]) :
     Submartingale f ℱ μ := by
   refine' ⟨hadp, fun i j hij => _, hint⟩
@@ -366,7 +366,7 @@ theorem Submartingale.condexp_sub_nonneg {f : ι → Ω → ℝ} (hf : Submartin
   · exact h
 #align measure_theory.submartingale.condexp_sub_nonneg MeasureTheory.Submartingale.condexp_sub_nonneg
 
-theorem submartingale_iff_condexp_sub_nonneg [IsFiniteMeasure μ] {f : ι → Ω → ℝ} :
+theorem submartingale_iff_condexp_sub_nonneg [FiniteMeasure μ] {f : ι → Ω → ℝ} :
     Submartingale f ℱ μ ↔
       Adapted ℱ f ∧ (∀ i, Integrable (f i) μ) ∧ ∀ i j, i ≤ j → 0 ≤ᵐ[μ] μ[f j - f i|ℱ i] :=
   ⟨fun h => ⟨h.Adapted, h.Integrable, fun i j => h.condexp_sub_nonneg⟩, fun ⟨hadp, hint, h⟩ =>
@@ -453,8 +453,8 @@ section Nat
 
 variable {𝒢 : Filtration ℕ m0}
 
-theorem submartingale_of_set_integral_le_succ [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
-    (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
+theorem submartingale_of_set_integral_le_succ [FiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
+    (hint : ∀ i, Integrable (f i) μ)
     (hf :
       ∀ i, ∀ s : Set Ω, measurable_set[𝒢 i] s → (∫ ω in s, f i ω ∂μ) ≤ ∫ ω in s, f (i + 1) ω ∂μ) :
     Submartingale f 𝒢 μ :=
@@ -465,7 +465,7 @@ theorem submartingale_of_set_integral_le_succ [IsFiniteMeasure μ] {f : ℕ →
   · exact le_trans hk₂ (hf k s (𝒢.mono hk₁ _ hs))
 #align measure_theory.submartingale_of_set_integral_le_succ MeasureTheory.submartingale_of_set_integral_le_succ
 
-theorem supermartingale_of_set_integral_succ_le [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
+theorem supermartingale_of_set_integral_succ_le [FiniteMeasure μ] {f : ℕ → Ω → ℝ}
     (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
     (hf :
       ∀ i, ∀ s : Set Ω, measurable_set[𝒢 i] s → (∫ ω in s, f (i + 1) ω ∂μ) ≤ ∫ ω in s, f i ω ∂μ) :
@@ -475,7 +475,7 @@ theorem supermartingale_of_set_integral_succ_le [IsFiniteMeasure μ] {f : ℕ 
   simpa only [integral_neg, Pi.neg_apply, neg_le_neg_iff]
 #align measure_theory.supermartingale_of_set_integral_succ_le MeasureTheory.supermartingale_of_set_integral_succ_le
 
-theorem martingale_of_set_integral_eq_succ [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
+theorem martingale_of_set_integral_eq_succ [FiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ)
     (hf :
       ∀ i, ∀ s : Set Ω, measurable_set[𝒢 i] s → (∫ ω in s, f i ω ∂μ) = ∫ ω in s, f (i + 1) ω ∂μ) :
@@ -485,7 +485,7 @@ theorem martingale_of_set_integral_eq_succ [IsFiniteMeasure μ] {f : ℕ → Ω
       submartingale_of_set_integral_le_succ hadp hint fun i s hs => (hf i s hs).le⟩
 #align measure_theory.martingale_of_set_integral_eq_succ MeasureTheory.martingale_of_set_integral_eq_succ
 
-theorem submartingale_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
+theorem submartingale_nat [FiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i, f i ≤ᵐ[μ] μ[f (i + 1)|𝒢 i]) : Submartingale f 𝒢 μ :=
   by
   refine' submartingale_of_set_integral_le_succ hadp hint fun i s hs => _
@@ -495,7 +495,7 @@ theorem submartingale_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp :
   exact set_integral_mono_ae (hint i).IntegrableOn integrable_condexp.integrable_on (hf i)
 #align measure_theory.submartingale_nat MeasureTheory.submartingale_nat
 
-theorem supermartingale_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
+theorem supermartingale_nat [FiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i, μ[f (i + 1)|𝒢 i] ≤ᵐ[μ] f i) :
     Supermartingale f 𝒢 μ := by
   rw [← neg_neg f]
@@ -505,14 +505,14 @@ theorem supermartingale_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp
   filter_upwards [hf i]with x hx using neg_le_neg hx
 #align measure_theory.supermartingale_nat MeasureTheory.supermartingale_nat
 
-theorem martingale_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
+theorem martingale_nat [FiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i, f i =ᵐ[μ] μ[f (i + 1)|𝒢 i]) : Martingale f 𝒢 μ :=
   martingale_iff.2
     ⟨supermartingale_nat hadp hint fun i => (hf i).symm.le,
       submartingale_nat hadp hint fun i => (hf i).le⟩
 #align measure_theory.martingale_nat MeasureTheory.martingale_nat
 
-theorem submartingale_of_condexp_sub_nonneg_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
+theorem submartingale_of_condexp_sub_nonneg_nat [FiniteMeasure μ] {f : ℕ → Ω → ℝ}
     (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
     (hf : ∀ i, 0 ≤ᵐ[μ] μ[f (i + 1) - f i|𝒢 i]) : Submartingale f 𝒢 μ :=
   by
@@ -522,7 +522,7 @@ theorem submartingale_of_condexp_sub_nonneg_nat [IsFiniteMeasure μ] {f : ℕ 
   infer_instance
 #align measure_theory.submartingale_of_condexp_sub_nonneg_nat MeasureTheory.submartingale_of_condexp_sub_nonneg_nat
 
-theorem supermartingale_of_condexp_sub_nonneg_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
+theorem supermartingale_of_condexp_sub_nonneg_nat [FiniteMeasure μ] {f : ℕ → Ω → ℝ}
     (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
     (hf : ∀ i, 0 ≤ᵐ[μ] μ[f i - f (i + 1)|𝒢 i]) : Supermartingale f 𝒢 μ :=
   by
@@ -531,9 +531,9 @@ theorem supermartingale_of_condexp_sub_nonneg_nat [IsFiniteMeasure μ] {f : ℕ
   simpa only [Pi.zero_apply, Pi.neg_apply, neg_sub_neg]
 #align measure_theory.supermartingale_of_condexp_sub_nonneg_nat MeasureTheory.supermartingale_of_condexp_sub_nonneg_nat
 
-theorem martingale_of_condexp_sub_eq_zero_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
-    (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
-    (hf : ∀ i, μ[f (i + 1) - f i|𝒢 i] =ᵐ[μ] 0) : Martingale f 𝒢 μ :=
+theorem martingale_of_condexp_sub_eq_zero_nat [FiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
+    (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i, μ[f (i + 1) - f i|𝒢 i] =ᵐ[μ] 0) :
+    Martingale f 𝒢 μ :=
   by
   refine'
     martingale_iff.2
@@ -604,7 +604,7 @@ theorem integrable_stoppedValue [LE E] {f : ℕ → Ω → E} (hf : Submartingal
 
 end Submartingale
 
-theorem Submartingale.sum_mul_sub [IsFiniteMeasure μ] {R : ℝ} {ξ f : ℕ → Ω → ℝ}
+theorem Submartingale.sum_mul_sub [FiniteMeasure μ] {R : ℝ} {ξ f : ℕ → Ω → ℝ}
     (hf : Submartingale f 𝒢 μ) (hξ : Adapted 𝒢 ξ) (hbdd : ∀ n ω, ξ n ω ≤ R)
     (hnonneg : ∀ n ω, 0 ≤ ξ n ω) :
     Submartingale (fun n => ∑ k in Finset.range n, ξ k * (f (k + 1) - f k)) 𝒢 μ :=
@@ -640,7 +640,7 @@ theorem Submartingale.sum_mul_sub [IsFiniteMeasure μ] {R : ℝ} {ξ f : ℕ →
 /-- Given a discrete submartingale `f` and a predictable process `ξ` (i.e. `ξ (n + 1)` is adapted)
 the process defined by `λ n, ∑ k in finset.range n, ξ (k + 1) * (f (k + 1) - f k)` is also a
 submartingale. -/
-theorem Submartingale.sum_mul_sub' [IsFiniteMeasure μ] {R : ℝ} {ξ f : ℕ → Ω → ℝ}
+theorem Submartingale.sum_mul_sub' [FiniteMeasure μ] {R : ℝ} {ξ f : ℕ → Ω → ℝ}
     (hf : Submartingale f 𝒢 μ) (hξ : Adapted 𝒢 fun n => ξ (n + 1)) (hbdd : ∀ n ω, ξ n ω ≤ R)
     (hnonneg : ∀ n ω, 0 ≤ ξ n ω) :
     Submartingale (fun n => ∑ k in Finset.range n, ξ (k + 1) * (f (k + 1) - f k)) 𝒢 μ :=

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

@@ -73,28 +73,28 @@ def Submartingale [LE E] (f : ι → Ω → E) (ℱ : Filtration ι m0)
   Adapted ℱ f ∧ (∀ i j, i ≤ j → f i ≤ᵐ[μ] μ[f j|ℱ i]) ∧ ∀ i, Integrable (f i) μ
 #align measure_theory.submartingale MeasureTheory.Submartingale
 
-theorem martingaleConst (ℱ : Filtration ι m0) (μ : Measure Ω) [IsFiniteMeasure μ] (x : E) :
+theorem martingale_const (ℱ : Filtration ι m0) (μ : Measure Ω) [IsFiniteMeasure μ] (x : E) :
     Martingale (fun _ _ => x) ℱ μ :=
   ⟨adapted_const ℱ _, fun i j hij => by rw [condexp_const (ℱ.le _)]⟩
-#align measure_theory.martingale_const MeasureTheory.martingaleConst
+#align measure_theory.martingale_const MeasureTheory.martingale_const
 
-theorem martingaleConstFun [OrderBot ι] (ℱ : Filtration ι m0) (μ : Measure Ω) [IsFiniteMeasure μ]
+theorem martingale_const_fun [OrderBot ι] (ℱ : Filtration ι m0) (μ : Measure Ω) [IsFiniteMeasure μ]
     {f : Ω → E} (hf : strongly_measurable[ℱ ⊥] f) (hfint : Integrable f μ) :
     Martingale (fun _ => f) ℱ μ :=
   by
   refine' ⟨fun i => hf.mono <| ℱ.mono bot_le, fun i j hij => _⟩
   rw [condexp_of_strongly_measurable (ℱ.le _) (hf.mono <| ℱ.mono bot_le) hfint]
   infer_instance
-#align measure_theory.martingale_const_fun MeasureTheory.martingaleConstFun
+#align measure_theory.martingale_const_fun MeasureTheory.martingale_const_fun
 
 variable (E)
 
-theorem martingaleZero (ℱ : Filtration ι m0) (μ : Measure Ω) : Martingale (0 : ι → Ω → E) ℱ μ :=
+theorem martingale_zero (ℱ : Filtration ι m0) (μ : Measure Ω) : Martingale (0 : ι → Ω → E) ℱ μ :=
   ⟨adapted_zero E ℱ, fun i j hij =>
     by
     rw [Pi.zero_apply, condexp_zero]
     simp⟩
-#align measure_theory.martingale_zero MeasureTheory.martingaleZero
+#align measure_theory.martingale_zero MeasureTheory.martingale_zero
 
 variable {E}
 
@@ -116,7 +116,7 @@ theorem condexp_ae_eq (hf : Martingale f ℱ μ) {i j : ι} (hij : i ≤ j) : μ
 
 @[protected]
 theorem integrable (hf : Martingale f ℱ μ) (i : ι) : Integrable (f i) μ :=
-  integrableCondexp.congr (hf.condexp_ae_eq (le_refl i))
+  integrable_condexp.congr (hf.condexp_ae_eq (le_refl i))
 #align measure_theory.martingale.integrable MeasureTheory.Martingale.integrable
 
 theorem set_integral_eq [SigmaFiniteFiltration μ ℱ] (hf : Martingale f ℱ μ) {i j : ι} (hij : i ≤ j)
@@ -166,10 +166,10 @@ theorem martingale_iff [PartialOrder E] :
     ⟨hf₁.1, fun i j hij => (hf₁.2.1 i j hij).antisymm (hf₂.2.1 i j hij)⟩⟩
 #align measure_theory.martingale_iff MeasureTheory.martingale_iff
 
-theorem martingaleCondexp (f : Ω → E) (ℱ : Filtration ι m0) (μ : Measure Ω)
+theorem martingale_condexp (f : Ω → E) (ℱ : Filtration ι m0) (μ : Measure Ω)
     [SigmaFiniteFiltration μ ℱ] : Martingale (fun i => μ[f|ℱ i]) ℱ μ :=
   ⟨fun i => stronglyMeasurable_condexp, fun i j hij => condexp_condexp_of_le (ℱ.mono hij) (ℱ.le j)⟩
-#align measure_theory.martingale_condexp MeasureTheory.martingaleCondexp
+#align measure_theory.martingale_condexp MeasureTheory.martingale_condexp
 
 namespace Supermartingale
 
@@ -213,10 +213,10 @@ theorem add [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Superm
   refine' add_le_add _ _ <;> assumption
 #align measure_theory.supermartingale.add MeasureTheory.Supermartingale.add
 
-theorem addMartingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Supermartingale f ℱ μ)
-    (hg : Martingale g ℱ μ) : Supermartingale (f + g) ℱ μ :=
+theorem add_martingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)]
+    (hf : Supermartingale f ℱ μ) (hg : Martingale g ℱ μ) : Supermartingale (f + g) ℱ μ :=
   hf.add hg.Supermartingale
-#align measure_theory.supermartingale.add_martingale MeasureTheory.Supermartingale.addMartingale
+#align measure_theory.supermartingale.add_martingale MeasureTheory.Supermartingale.add_martingale
 
 theorem neg [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Supermartingale f ℱ μ) :
     Submartingale (-f) ℱ μ :=
@@ -262,10 +262,10 @@ theorem add [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Submar
   refine' add_le_add _ _ <;> assumption
 #align measure_theory.submartingale.add MeasureTheory.Submartingale.add
 
-theorem addMartingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Submartingale f ℱ μ)
+theorem add_martingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Submartingale f ℱ μ)
     (hg : Martingale g ℱ μ) : Submartingale (f + g) ℱ μ :=
   hf.add hg.Submartingale
-#align measure_theory.submartingale.add_martingale MeasureTheory.Submartingale.addMartingale
+#align measure_theory.submartingale.add_martingale MeasureTheory.Submartingale.add_martingale
 
 theorem neg [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Submartingale f ℱ μ) :
     Supermartingale (-f) ℱ μ :=
@@ -284,17 +284,17 @@ theorem set_integral_le [SigmaFiniteFiltration μ ℱ] {f : ι → Ω → ℝ} (
   exact supermartingale.set_integral_le hf.neg hij hs
 #align measure_theory.submartingale.set_integral_le MeasureTheory.Submartingale.set_integral_le
 
-theorem subSupermartingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)]
+theorem sub_supermartingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)]
     (hf : Submartingale f ℱ μ) (hg : Supermartingale g ℱ μ) : Submartingale (f - g) ℱ μ :=
   by
   rw [sub_eq_add_neg]
   exact hf.add hg.neg
-#align measure_theory.submartingale.sub_supermartingale MeasureTheory.Submartingale.subSupermartingale
+#align measure_theory.submartingale.sub_supermartingale MeasureTheory.Submartingale.sub_supermartingale
 
-theorem subMartingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Submartingale f ℱ μ)
+theorem sub_martingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Submartingale f ℱ μ)
     (hg : Martingale g ℱ μ) : Submartingale (f - g) ℱ μ :=
-  hf.subSupermartingale hg.Supermartingale
-#align measure_theory.submartingale.sub_martingale MeasureTheory.Submartingale.subMartingale
+  hf.sub_supermartingale hg.Supermartingale
+#align measure_theory.submartingale.sub_martingale MeasureTheory.Submartingale.sub_martingale
 
 protected theorem sup {f g : ι → Ω → ℝ} (hf : Submartingale f ℱ μ) (hg : Submartingale g ℱ μ) :
     Submartingale (f ⊔ g) ℱ μ :=
@@ -316,14 +316,14 @@ protected theorem sup {f g : ι → Ω → ℝ} (hf : Submartingale f ℱ μ) (h
 #align measure_theory.submartingale.sup MeasureTheory.Submartingale.sup
 
 protected theorem pos {f : ι → Ω → ℝ} (hf : Submartingale f ℱ μ) : Submartingale (f⁺) ℱ μ :=
-  hf.sup (martingaleZero _ _ _).Submartingale
+  hf.sup (martingale_zero _ _ _).Submartingale
 #align measure_theory.submartingale.pos MeasureTheory.Submartingale.pos
 
 end Submartingale
 
 section Submartingale
 
-theorem submartingaleOfSetIntegralLe [IsFiniteMeasure μ] {f : ι → Ω → ℝ} (hadp : Adapted ℱ f)
+theorem submartingale_of_set_integral_le [IsFiniteMeasure μ] {f : ι → Ω → ℝ} (hadp : Adapted ℱ f)
     (hint : ∀ i, Integrable (f i) μ)
     (hf :
       ∀ i j : ι,
@@ -343,16 +343,16 @@ theorem submartingaleOfSetIntegralLe [IsFiniteMeasure μ] {f : ι → Ω → ℝ
   rwa [← set_integral_trim _ (strongly_measurable_condexp.sub <| hadp i) hs,
     integral_sub' integrable_condexp.integrable_on (hint i).IntegrableOn, sub_nonneg,
     set_integral_condexp (ℱ.le i) (hint j) hs]
-#align measure_theory.submartingale_of_set_integral_le MeasureTheory.submartingaleOfSetIntegralLe
+#align measure_theory.submartingale_of_set_integral_le MeasureTheory.submartingale_of_set_integral_le
 
-theorem submartingaleOfCondexpSubNonneg [IsFiniteMeasure μ] {f : ι → Ω → ℝ} (hadp : Adapted ℱ f)
+theorem submartingale_of_condexp_sub_nonneg [IsFiniteMeasure μ] {f : ι → Ω → ℝ} (hadp : Adapted ℱ f)
     (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i j, i ≤ j → 0 ≤ᵐ[μ] μ[f j - f i|ℱ i]) :
     Submartingale f ℱ μ := by
   refine' ⟨hadp, fun i j hij => _, hint⟩
   rw [← condexp_of_strongly_measurable (ℱ.le _) (hadp _) (hint _), ← eventually_sub_nonneg]
   exact eventually_le.trans (hf i j hij) (condexp_sub (hint _) (hint _)).le
   infer_instance
-#align measure_theory.submartingale_of_condexp_sub_nonneg MeasureTheory.submartingaleOfCondexpSubNonneg
+#align measure_theory.submartingale_of_condexp_sub_nonneg MeasureTheory.submartingale_of_condexp_sub_nonneg
 
 theorem Submartingale.condexp_sub_nonneg {f : ι → Ω → ℝ} (hf : Submartingale f ℱ μ) {i j : ι}
     (hij : i ≤ j) : 0 ≤ᵐ[μ] μ[f j - f i|ℱ i] :=
@@ -370,31 +370,31 @@ theorem submartingale_iff_condexp_sub_nonneg [IsFiniteMeasure μ] {f : ι → Ω
     Submartingale f ℱ μ ↔
       Adapted ℱ f ∧ (∀ i, Integrable (f i) μ) ∧ ∀ i j, i ≤ j → 0 ≤ᵐ[μ] μ[f j - f i|ℱ i] :=
   ⟨fun h => ⟨h.Adapted, h.Integrable, fun i j => h.condexp_sub_nonneg⟩, fun ⟨hadp, hint, h⟩ =>
-    submartingaleOfCondexpSubNonneg hadp hint h⟩
+    submartingale_of_condexp_sub_nonneg hadp hint h⟩
 #align measure_theory.submartingale_iff_condexp_sub_nonneg MeasureTheory.submartingale_iff_condexp_sub_nonneg
 
 end Submartingale
 
 namespace Supermartingale
 
-theorem subSubmartingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)]
+theorem sub_submartingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)]
     (hf : Supermartingale f ℱ μ) (hg : Submartingale g ℱ μ) : Supermartingale (f - g) ℱ μ :=
   by
   rw [sub_eq_add_neg]
   exact hf.add hg.neg
-#align measure_theory.supermartingale.sub_submartingale MeasureTheory.Supermartingale.subSubmartingale
+#align measure_theory.supermartingale.sub_submartingale MeasureTheory.Supermartingale.sub_submartingale
 
-theorem subMartingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Supermartingale f ℱ μ)
-    (hg : Martingale g ℱ μ) : Supermartingale (f - g) ℱ μ :=
-  hf.subSubmartingale hg.Submartingale
-#align measure_theory.supermartingale.sub_martingale MeasureTheory.Supermartingale.subMartingale
+theorem sub_martingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)]
+    (hf : Supermartingale f ℱ μ) (hg : Martingale g ℱ μ) : Supermartingale (f - g) ℱ μ :=
+  hf.sub_submartingale hg.Submartingale
+#align measure_theory.supermartingale.sub_martingale MeasureTheory.Supermartingale.sub_martingale
 
 section
 
 variable {F : Type _} [NormedLatticeAddCommGroup F] [NormedSpace ℝ F] [CompleteSpace F]
   [OrderedSMul ℝ F]
 
-theorem smulNonneg {f : ι → Ω → F} {c : ℝ} (hc : 0 ≤ c) (hf : Supermartingale f ℱ μ) :
+theorem smul_nonneg {f : ι → Ω → F} {c : ℝ} (hc : 0 ≤ c) (hf : Supermartingale f ℱ μ) :
     Supermartingale (c • f) ℱ μ :=
   by
   refine' ⟨hf.1.smul c, fun i j hij => _, fun i => (hf.2.2 i).smul c⟩
@@ -402,9 +402,9 @@ theorem smulNonneg {f : ι → Ω → F} {c : ℝ} (hc : 0 ≤ c) (hf : Supermar
   filter_upwards [hf.2.1 i j hij]with _ hle
   simp
   exact smul_le_smul_of_nonneg hle hc
-#align measure_theory.supermartingale.smul_nonneg MeasureTheory.Supermartingale.smulNonneg
+#align measure_theory.supermartingale.smul_nonneg MeasureTheory.Supermartingale.smul_nonneg
 
-theorem smulNonpos {f : ι → Ω → F} {c : ℝ} (hc : c ≤ 0) (hf : Supermartingale f ℱ μ) :
+theorem smul_nonpos {f : ι → Ω → F} {c : ℝ} (hc : c ≤ 0) (hf : Supermartingale f ℱ μ) :
     Submartingale (c • f) ℱ μ :=
   by
   rw [← neg_neg c,
@@ -412,7 +412,7 @@ theorem smulNonpos {f : ι → Ω → F} {c : ℝ} (hc : c ≤ 0) (hf : Supermar
       ext (i x)
       simp : - -c • f = -(-c • f))]
   exact (hf.smul_nonneg <| neg_nonneg.2 hc).neg
-#align measure_theory.supermartingale.smul_nonpos MeasureTheory.Supermartingale.smulNonpos
+#align measure_theory.supermartingale.smul_nonpos MeasureTheory.Supermartingale.smul_nonpos
 
 end
 
@@ -425,7 +425,7 @@ section
 variable {F : Type _} [NormedLatticeAddCommGroup F] [NormedSpace ℝ F] [CompleteSpace F]
   [OrderedSMul ℝ F]
 
-theorem smulNonneg {f : ι → Ω → F} {c : ℝ} (hc : 0 ≤ c) (hf : Submartingale f ℱ μ) :
+theorem smul_nonneg {f : ι → Ω → F} {c : ℝ} (hc : 0 ≤ c) (hf : Submartingale f ℱ μ) :
     Submartingale (c • f) ℱ μ :=
   by
   rw [← neg_neg c,
@@ -433,9 +433,9 @@ theorem smulNonneg {f : ι → Ω → F} {c : ℝ} (hc : 0 ≤ c) (hf : Submarti
       ext (i x)
       simp : - -c • f = -(c • -f))]
   exact supermartingale.neg (hf.neg.smul_nonneg hc)
-#align measure_theory.submartingale.smul_nonneg MeasureTheory.Submartingale.smulNonneg
+#align measure_theory.submartingale.smul_nonneg MeasureTheory.Submartingale.smul_nonneg
 
-theorem smulNonpos {f : ι → Ω → F} {c : ℝ} (hc : c ≤ 0) (hf : Submartingale f ℱ μ) :
+theorem smul_nonpos {f : ι → Ω → F} {c : ℝ} (hc : c ≤ 0) (hf : Submartingale f ℱ μ) :
     Supermartingale (c • f) ℱ μ :=
   by
   rw [← neg_neg c,
@@ -443,7 +443,7 @@ theorem smulNonpos {f : ι → Ω → F} {c : ℝ} (hc : c ≤ 0) (hf : Submarti
       ext (i x)
       simp : - -c • f = -(-c • f))]
   exact (hf.smul_nonneg <| neg_nonneg.2 hc).neg
-#align measure_theory.submartingale.smul_nonpos MeasureTheory.Submartingale.smulNonpos
+#align measure_theory.submartingale.smul_nonpos MeasureTheory.Submartingale.smul_nonpos
 
 end
 
@@ -453,8 +453,8 @@ section Nat
 
 variable {𝒢 : Filtration ℕ m0}
 
-theorem submartingaleOfSetIntegralLeSucc [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
-    (hint : ∀ i, Integrable (f i) μ)
+theorem submartingale_of_set_integral_le_succ [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
+    (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
     (hf :
       ∀ i, ∀ s : Set Ω, measurable_set[𝒢 i] s → (∫ ω in s, f i ω ∂μ) ≤ ∫ ω in s, f (i + 1) ω ∂μ) :
     Submartingale f 𝒢 μ :=
@@ -463,29 +463,29 @@ theorem submartingaleOfSetIntegralLeSucc [IsFiniteMeasure μ] {f : ℕ → Ω 
   induction' hij with k hk₁ hk₂
   · exact le_rfl
   · exact le_trans hk₂ (hf k s (𝒢.mono hk₁ _ hs))
-#align measure_theory.submartingale_of_set_integral_le_succ MeasureTheory.submartingaleOfSetIntegralLeSucc
+#align measure_theory.submartingale_of_set_integral_le_succ MeasureTheory.submartingale_of_set_integral_le_succ
 
-theorem supermartingaleOfSetIntegralSuccLe [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
-    (hint : ∀ i, Integrable (f i) μ)
+theorem supermartingale_of_set_integral_succ_le [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
+    (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
     (hf :
       ∀ i, ∀ s : Set Ω, measurable_set[𝒢 i] s → (∫ ω in s, f (i + 1) ω ∂μ) ≤ ∫ ω in s, f i ω ∂μ) :
     Supermartingale f 𝒢 μ := by
   rw [← neg_neg f]
   refine' (submartingale_of_set_integral_le_succ hadp.neg (fun i => (hint i).neg) _).neg
   simpa only [integral_neg, Pi.neg_apply, neg_le_neg_iff]
-#align measure_theory.supermartingale_of_set_integral_succ_le MeasureTheory.supermartingaleOfSetIntegralSuccLe
+#align measure_theory.supermartingale_of_set_integral_succ_le MeasureTheory.supermartingale_of_set_integral_succ_le
 
-theorem martingaleOfSetIntegralEqSucc [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
+theorem martingale_of_set_integral_eq_succ [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ)
     (hf :
       ∀ i, ∀ s : Set Ω, measurable_set[𝒢 i] s → (∫ ω in s, f i ω ∂μ) = ∫ ω in s, f (i + 1) ω ∂μ) :
     Martingale f 𝒢 μ :=
   martingale_iff.2
-    ⟨supermartingaleOfSetIntegralSuccLe hadp hint fun i s hs => (hf i s hs).ge,
-      submartingaleOfSetIntegralLeSucc hadp hint fun i s hs => (hf i s hs).le⟩
-#align measure_theory.martingale_of_set_integral_eq_succ MeasureTheory.martingaleOfSetIntegralEqSucc
+    ⟨supermartingale_of_set_integral_succ_le hadp hint fun i s hs => (hf i s hs).ge,
+      submartingale_of_set_integral_le_succ hadp hint fun i s hs => (hf i s hs).le⟩
+#align measure_theory.martingale_of_set_integral_eq_succ MeasureTheory.martingale_of_set_integral_eq_succ
 
-theorem submartingaleNat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
+theorem submartingale_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i, f i ≤ᵐ[μ] μ[f (i + 1)|𝒢 i]) : Submartingale f 𝒢 μ :=
   by
   refine' submartingale_of_set_integral_le_succ hadp hint fun i s hs => _
@@ -493,9 +493,9 @@ theorem submartingaleNat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : A
     (set_integral_condexp (𝒢.le i) (hint _) hs).symm
   rw [this]
   exact set_integral_mono_ae (hint i).IntegrableOn integrable_condexp.integrable_on (hf i)
-#align measure_theory.submartingale_nat MeasureTheory.submartingaleNat
+#align measure_theory.submartingale_nat MeasureTheory.submartingale_nat
 
-theorem supermartingaleNat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
+theorem supermartingale_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i, μ[f (i + 1)|𝒢 i] ≤ᵐ[μ] f i) :
     Supermartingale f 𝒢 μ := by
   rw [← neg_neg f]
@@ -503,37 +503,37 @@ theorem supermartingaleNat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp :
     (submartingale_nat hadp.neg (fun i => (hint i).neg) fun i =>
         eventually_le.trans _ (condexp_neg _).symm.le).neg
   filter_upwards [hf i]with x hx using neg_le_neg hx
-#align measure_theory.supermartingale_nat MeasureTheory.supermartingaleNat
+#align measure_theory.supermartingale_nat MeasureTheory.supermartingale_nat
 
-theorem martingaleNat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
+theorem martingale_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i, f i =ᵐ[μ] μ[f (i + 1)|𝒢 i]) : Martingale f 𝒢 μ :=
   martingale_iff.2
-    ⟨supermartingaleNat hadp hint fun i => (hf i).symm.le,
-      submartingaleNat hadp hint fun i => (hf i).le⟩
-#align measure_theory.martingale_nat MeasureTheory.martingaleNat
+    ⟨supermartingale_nat hadp hint fun i => (hf i).symm.le,
+      submartingale_nat hadp hint fun i => (hf i).le⟩
+#align measure_theory.martingale_nat MeasureTheory.martingale_nat
 
-theorem submartingaleOfCondexpSubNonnegNat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
-    (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i, 0 ≤ᵐ[μ] μ[f (i + 1) - f i|𝒢 i]) :
-    Submartingale f 𝒢 μ :=
+theorem submartingale_of_condexp_sub_nonneg_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
+    (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
+    (hf : ∀ i, 0 ≤ᵐ[μ] μ[f (i + 1) - f i|𝒢 i]) : Submartingale f 𝒢 μ :=
   by
   refine' submartingale_nat hadp hint fun i => _
   rw [← condexp_of_strongly_measurable (𝒢.le _) (hadp _) (hint _), ← eventually_sub_nonneg]
   exact eventually_le.trans (hf i) (condexp_sub (hint _) (hint _)).le
   infer_instance
-#align measure_theory.submartingale_of_condexp_sub_nonneg_nat MeasureTheory.submartingaleOfCondexpSubNonnegNat
+#align measure_theory.submartingale_of_condexp_sub_nonneg_nat MeasureTheory.submartingale_of_condexp_sub_nonneg_nat
 
-theorem supermartingaleOfCondexpSubNonnegNat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
+theorem supermartingale_of_condexp_sub_nonneg_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
     (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
     (hf : ∀ i, 0 ≤ᵐ[μ] μ[f i - f (i + 1)|𝒢 i]) : Supermartingale f 𝒢 μ :=
   by
   rw [← neg_neg f]
   refine' (submartingale_of_condexp_sub_nonneg_nat hadp.neg (fun i => (hint i).neg) _).neg
   simpa only [Pi.zero_apply, Pi.neg_apply, neg_sub_neg]
-#align measure_theory.supermartingale_of_condexp_sub_nonneg_nat MeasureTheory.supermartingaleOfCondexpSubNonnegNat
+#align measure_theory.supermartingale_of_condexp_sub_nonneg_nat MeasureTheory.supermartingale_of_condexp_sub_nonneg_nat
 
-theorem martingaleOfCondexpSubEqZeroNat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
-    (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i, μ[f (i + 1) - f i|𝒢 i] =ᵐ[μ] 0) :
-    Martingale f 𝒢 μ :=
+theorem martingale_of_condexp_sub_eq_zero_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
+    (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
+    (hf : ∀ i, μ[f (i + 1) - f i|𝒢 i] =ᵐ[μ] 0) : Martingale f 𝒢 μ :=
   by
   refine'
     martingale_iff.2
@@ -543,7 +543,7 @@ theorem martingaleOfCondexpSubEqZeroNat [IsFiniteMeasure μ] {f : ℕ → Ω →
   refine' (eventually_eq.trans _ (condexp_neg _).symm).le
   filter_upwards [hf i]with x hx
   simpa only [Pi.zero_apply, Pi.neg_apply, zero_eq_neg]
-#align measure_theory.martingale_of_condexp_sub_eq_zero_nat MeasureTheory.martingaleOfCondexpSubEqZeroNat
+#align measure_theory.martingale_of_condexp_sub_eq_zero_nat MeasureTheory.martingale_of_condexp_sub_eq_zero_nat
 
 -- Note that one cannot use `submartingale.zero_le_of_predictable` to prove the other two
 -- corresponding lemmas without imposing more restrictions to the ordering of `E`
@@ -597,14 +597,14 @@ theorem Martingale.eq_zero_of_predictable [SigmaFiniteFiltration μ 𝒢] {f : 
 namespace Submartingale
 
 @[protected]
-theorem integrableStoppedValue [LE E] {f : ℕ → Ω → E} (hf : Submartingale f 𝒢 μ) {τ : Ω → ℕ}
+theorem integrable_stoppedValue [LE E] {f : ℕ → Ω → E} (hf : Submartingale f 𝒢 μ) {τ : Ω → ℕ}
     (hτ : IsStoppingTime 𝒢 τ) {N : ℕ} (hbdd : ∀ ω, τ ω ≤ N) : Integrable (stoppedValue f τ) μ :=
-  integrableStoppedValue ℕ hτ hf.Integrable hbdd
-#align measure_theory.submartingale.integrable_stopped_value MeasureTheory.Submartingale.integrableStoppedValue
+  integrable_stoppedValue ℕ hτ hf.Integrable hbdd
+#align measure_theory.submartingale.integrable_stopped_value MeasureTheory.Submartingale.integrable_stoppedValue
 
 end Submartingale
 
-theorem Submartingale.sumMulSub [IsFiniteMeasure μ] {R : ℝ} {ξ f : ℕ → Ω → ℝ}
+theorem Submartingale.sum_mul_sub [IsFiniteMeasure μ] {R : ℝ} {ξ f : ℕ → Ω → ℝ}
     (hf : Submartingale f 𝒢 μ) (hξ : Adapted 𝒢 ξ) (hbdd : ∀ n ω, ξ n ω ≤ R)
     (hnonneg : ∀ n ω, 0 ≤ ξ n ω) :
     Submartingale (fun n => ∑ k in Finset.range n, ξ k * (f (k + 1) - f k)) 𝒢 μ :=
@@ -632,20 +632,20 @@ theorem Submartingale.sumMulSub [IsFiniteMeasure μ] {R : ℝ} {ξ f : ℕ → 
       (eventually_le.mul_nonneg (eventually_of_forall (hnonneg _))
         (hf.condexp_sub_nonneg (Nat.le_succ _)))
       (condexp_strongly_measurable_mul (hξ _)
-            (((hf.integrable _).sub (hf.integrable _)).bddMul
+            (((hf.integrable _).sub (hf.integrable _)).bdd_mul
               hξ.strongly_measurable.ae_strongly_measurable (hξbdd _))
             ((hf.integrable _).sub (hf.integrable _))).symm.le
-#align measure_theory.submartingale.sum_mul_sub MeasureTheory.Submartingale.sumMulSub
+#align measure_theory.submartingale.sum_mul_sub MeasureTheory.Submartingale.sum_mul_sub
 
 /-- Given a discrete submartingale `f` and a predictable process `ξ` (i.e. `ξ (n + 1)` is adapted)
 the process defined by `λ n, ∑ k in finset.range n, ξ (k + 1) * (f (k + 1) - f k)` is also a
 submartingale. -/
-theorem Submartingale.sumMulSub' [IsFiniteMeasure μ] {R : ℝ} {ξ f : ℕ → Ω → ℝ}
+theorem Submartingale.sum_mul_sub' [IsFiniteMeasure μ] {R : ℝ} {ξ f : ℕ → Ω → ℝ}
     (hf : Submartingale f 𝒢 μ) (hξ : Adapted 𝒢 fun n => ξ (n + 1)) (hbdd : ∀ n ω, ξ n ω ≤ R)
     (hnonneg : ∀ n ω, 0 ≤ ξ n ω) :
     Submartingale (fun n => ∑ k in Finset.range n, ξ (k + 1) * (f (k + 1) - f k)) 𝒢 μ :=
-  hf.sumMulSub hξ (fun n => hbdd _) fun n => hnonneg _
-#align measure_theory.submartingale.sum_mul_sub' MeasureTheory.Submartingale.sumMulSub'
+  hf.sum_mul_sub hξ (fun n => hbdd _) fun n => hnonneg _
+#align measure_theory.submartingale.sum_mul_sub' MeasureTheory.Submartingale.sum_mul_sub'
 
 end Nat
 

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

@@ -43,7 +43,7 @@ The definitions of filtration and adapted can be found in `probability.stopping`
 
 open TopologicalSpace Filter
 
-open NNReal Ennreal MeasureTheory ProbabilityTheory BigOperators
+open NNReal ENNReal MeasureTheory ProbabilityTheory BigOperators
 
 namespace MeasureTheory
 

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

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

@@ -106,12 +106,16 @@ protected theorem integrable (hf : Martingale f ℱ μ) (i : ι) : Integrable (f
   integrable_condexp.congr (hf.condexp_ae_eq (le_refl i))
 #align measure_theory.martingale.integrable MeasureTheory.Martingale.integrable
 
-theorem set_integral_eq [SigmaFiniteFiltration μ ℱ] (hf : Martingale f ℱ μ) {i j : ι} (hij : i ≤ j)
+theorem setIntegral_eq [SigmaFiniteFiltration μ ℱ] (hf : Martingale f ℱ μ) {i j : ι} (hij : i ≤ j)
     {s : Set Ω} (hs : MeasurableSet[ℱ i] s) : ∫ ω in s, f i ω ∂μ = ∫ ω in s, f j ω ∂μ := by
-  rw [← @set_integral_condexp _ _ _ _ _ (ℱ i) m0 _ _ _ (ℱ.le i) _ (hf.integrable j) hs]
-  refine' set_integral_congr_ae (ℱ.le i s hs) _
+  rw [← @setIntegral_condexp _ _ _ _ _ (ℱ i) m0 _ _ _ (ℱ.le i) _ (hf.integrable j) hs]
+  refine' setIntegral_congr_ae (ℱ.le i s hs) _
   filter_upwards [hf.2 i j hij] with _ heq _ using heq.symm
-#align measure_theory.martingale.set_integral_eq MeasureTheory.Martingale.set_integral_eq
+#align measure_theory.martingale.set_integral_eq MeasureTheory.Martingale.setIntegral_eq
+
+@[deprecated]
+alias set_integral_eq :=
+  setIntegral_eq -- deprecated on 2024-04-17
 
 theorem add (hf : Martingale f ℱ μ) (hg : Martingale g ℱ μ) : Martingale (f + g) ℱ μ := by
   refine' ⟨hf.adapted.add hg.adapted, fun i j hij => _⟩
@@ -173,13 +177,17 @@ theorem condexp_ae_le [LE E] (hf : Supermartingale f ℱ μ) {i j : ι} (hij : i
   hf.2.1 i j hij
 #align measure_theory.supermartingale.condexp_ae_le MeasureTheory.Supermartingale.condexp_ae_le
 
-theorem set_integral_le [SigmaFiniteFiltration μ ℱ] {f : ι → Ω → ℝ} (hf : Supermartingale f ℱ μ)
+theorem setIntegral_le [SigmaFiniteFiltration μ ℱ] {f : ι → Ω → ℝ} (hf : Supermartingale f ℱ μ)
     {i j : ι} (hij : i ≤ j) {s : Set Ω} (hs : MeasurableSet[ℱ i] s) :
     ∫ ω in s, f j ω ∂μ ≤ ∫ ω in s, f i ω ∂μ := by
-  rw [← set_integral_condexp (ℱ.le i) (hf.integrable j) hs]
-  refine' set_integral_mono_ae integrable_condexp.integrableOn (hf.integrable i).integrableOn _
+  rw [← setIntegral_condexp (ℱ.le i) (hf.integrable j) hs]
+  refine' setIntegral_mono_ae integrable_condexp.integrableOn (hf.integrable i).integrableOn _
   filter_upwards [hf.2.1 i j hij] with _ heq using heq
-#align measure_theory.supermartingale.set_integral_le MeasureTheory.Supermartingale.set_integral_le
+#align measure_theory.supermartingale.set_integral_le MeasureTheory.Supermartingale.setIntegral_le
+
+@[deprecated]
+alias set_integral_le :=
+  setIntegral_le -- deprecated on 2024-04-17
 
 theorem add [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Supermartingale f ℱ μ)
     (hg : Supermartingale g ℱ μ) : Supermartingale (f + g) ℱ μ := by
@@ -246,13 +254,17 @@ theorem neg [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)] (hf : Submar
   simpa
 #align measure_theory.submartingale.neg MeasureTheory.Submartingale.neg
 
-/-- The converse of this lemma is `MeasureTheory.submartingale_of_set_integral_le`. -/
-theorem set_integral_le [SigmaFiniteFiltration μ ℱ] {f : ι → Ω → ℝ} (hf : Submartingale f ℱ μ)
+/-- The converse of this lemma is `MeasureTheory.submartingale_of_setIntegral_le`. -/
+theorem setIntegral_le [SigmaFiniteFiltration μ ℱ] {f : ι → Ω → ℝ} (hf : Submartingale f ℱ μ)
     {i j : ι} (hij : i ≤ j) {s : Set Ω} (hs : MeasurableSet[ℱ i] s) :
     ∫ ω in s, f i ω ∂μ ≤ ∫ ω in s, f j ω ∂μ := by
   rw [← neg_le_neg_iff, ← integral_neg, ← integral_neg]
-  exact Supermartingale.set_integral_le hf.neg hij hs
-#align measure_theory.submartingale.set_integral_le MeasureTheory.Submartingale.set_integral_le
+  exact Supermartingale.setIntegral_le hf.neg hij hs
+#align measure_theory.submartingale.set_integral_le MeasureTheory.Submartingale.setIntegral_le
+
+@[deprecated]
+alias set_integral_le :=
+  setIntegral_le -- deprecated on 2024-04-17
 
 theorem sub_supermartingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)]
     (hf : Submartingale f ℱ μ) (hg : Supermartingale g ℱ μ) : Submartingale (f - g) ℱ μ := by
@@ -285,7 +297,7 @@ end Submartingale
 
 section Submartingale
 
-theorem submartingale_of_set_integral_le [IsFiniteMeasure μ] {f : ι → Ω → ℝ} (hadp : Adapted ℱ f)
+theorem submartingale_of_setIntegral_le [IsFiniteMeasure μ] {f : ι → Ω → ℝ} (hadp : Adapted ℱ f)
     (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i j : ι,
       i ≤ j → ∀ s : Set Ω, MeasurableSet[ℱ i] s → ∫ ω in s, f i ω ∂μ ≤ ∫ ω in s, f j ω ∂μ) :
     Submartingale f ℱ μ := by
@@ -294,14 +306,18 @@ theorem submartingale_of_set_integral_le [IsFiniteMeasure μ] {f : ι → Ω →
   suffices 0 ≤ᵐ[μ.trim (ℱ.le i)] μ[f j|ℱ i] - f i by
     filter_upwards [this] with x hx
     rwa [← sub_nonneg]
-  refine' ae_nonneg_of_forall_set_integral_nonneg
+  refine' ae_nonneg_of_forall_setIntegral_nonneg
     ((integrable_condexp.sub (hint i)).trim _ (stronglyMeasurable_condexp.sub <| hadp i))
       fun s hs _ => _
   specialize hf i j hij s hs
-  rwa [← set_integral_trim _ (stronglyMeasurable_condexp.sub <| hadp i) hs,
+  rwa [← setIntegral_trim _ (stronglyMeasurable_condexp.sub <| hadp i) hs,
     integral_sub' integrable_condexp.integrableOn (hint i).integrableOn, sub_nonneg,
-    set_integral_condexp (ℱ.le i) (hint j) hs]
-#align measure_theory.submartingale_of_set_integral_le MeasureTheory.submartingale_of_set_integral_le
+    setIntegral_condexp (ℱ.le i) (hint j) hs]
+#align measure_theory.submartingale_of_set_integral_le MeasureTheory.submartingale_of_setIntegral_le
+
+@[deprecated]
+alias submartingale_of_set_integral_le :=
+  submartingale_of_setIntegral_le -- deprecated on 2024-04-17
 
 theorem submartingale_of_condexp_sub_nonneg [IsFiniteMeasure μ] {f : ι → Ω → ℝ} (hadp : Adapted ℱ f)
     (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i j, i ≤ j → 0 ≤ᵐ[μ] μ[f j - f i|ℱ i]) :
@@ -393,41 +409,53 @@ section Nat
 
 variable {𝒢 : Filtration ℕ m0}
 
-theorem submartingale_of_set_integral_le_succ [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
+theorem submartingale_of_setIntegral_le_succ [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
     (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
     (hf : ∀ i, ∀ s : Set Ω, MeasurableSet[𝒢 i] s → ∫ ω in s, f i ω ∂μ ≤ ∫ ω in s, f (i + 1) ω ∂μ) :
     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 => _
   induction' hij with k hk₁ hk₂
   · exact le_rfl
   · exact le_trans hk₂ (hf k s (𝒢.mono hk₁ _ hs))
-#align measure_theory.submartingale_of_set_integral_le_succ MeasureTheory.submartingale_of_set_integral_le_succ
+#align measure_theory.submartingale_of_set_integral_le_succ MeasureTheory.submartingale_of_setIntegral_le_succ
 
-theorem supermartingale_of_set_integral_succ_le [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
+@[deprecated]
+alias submartingale_of_set_integral_le_succ :=
+  submartingale_of_setIntegral_le_succ -- deprecated on 2024-04-17
+
+theorem supermartingale_of_setIntegral_succ_le [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ}
     (hadp : Adapted 𝒢 f) (hint : ∀ i, Integrable (f i) μ)
     (hf : ∀ i, ∀ s : Set Ω, MeasurableSet[𝒢 i] s → ∫ ω in s, f (i + 1) ω ∂μ ≤ ∫ ω in s, f i ω ∂μ) :
     Supermartingale f 𝒢 μ := by
   rw [← neg_neg f]
-  refine' (submartingale_of_set_integral_le_succ hadp.neg (fun i => (hint i).neg) _).neg
+  refine' (submartingale_of_setIntegral_le_succ hadp.neg (fun i => (hint i).neg) _).neg
   simpa only [integral_neg, Pi.neg_apply, neg_le_neg_iff]
-#align measure_theory.supermartingale_of_set_integral_succ_le MeasureTheory.supermartingale_of_set_integral_succ_le
+#align measure_theory.supermartingale_of_set_integral_succ_le MeasureTheory.supermartingale_of_setIntegral_succ_le
+
+@[deprecated]
+alias supermartingale_of_set_integral_succ_le :=
+  supermartingale_of_setIntegral_succ_le -- deprecated on 2024-04-17
 
-theorem martingale_of_set_integral_eq_succ [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
+theorem martingale_of_setIntegral_eq_succ [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ)
     (hf : ∀ i, ∀ s : Set Ω, MeasurableSet[𝒢 i] s → ∫ ω in s, f i ω ∂μ = ∫ ω in s, f (i + 1) ω ∂μ) :
     Martingale f 𝒢 μ :=
-  martingale_iff.2 ⟨supermartingale_of_set_integral_succ_le hadp hint fun i s hs => (hf i s hs).ge,
-    submartingale_of_set_integral_le_succ hadp hint fun i s hs => (hf i s hs).le⟩
-#align measure_theory.martingale_of_set_integral_eq_succ MeasureTheory.martingale_of_set_integral_eq_succ
+  martingale_iff.2 ⟨supermartingale_of_setIntegral_succ_le hadp hint fun i s hs => (hf i s hs).ge,
+    submartingale_of_setIntegral_le_succ hadp hint fun i s hs => (hf i s hs).le⟩
+#align measure_theory.martingale_of_set_integral_eq_succ MeasureTheory.martingale_of_setIntegral_eq_succ
+
+@[deprecated]
+alias martingale_of_set_integral_eq_succ :=
+  martingale_of_setIntegral_eq_succ -- deprecated on 2024-04-17
 
 theorem submartingale_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)
     (hint : ∀ i, Integrable (f i) μ) (hf : ∀ i, f i ≤ᵐ[μ] μ[f (i + 1)|𝒢 i]) :
     Submartingale f 𝒢 μ := by
-  refine' submartingale_of_set_integral_le_succ hadp hint fun i s hs => _
+  refine' submartingale_of_setIntegral_le_succ hadp hint fun i s hs => _
   have : ∫ ω in s, f (i + 1) ω ∂μ = ∫ ω in s, (μ[f (i + 1)|𝒢 i]) ω ∂μ :=
-    (set_integral_condexp (𝒢.le i) (hint _) hs).symm
+    (setIntegral_condexp (𝒢.le i) (hint _) hs).symm
   rw [this]
-  exact set_integral_mono_ae (hint i).integrableOn integrable_condexp.integrableOn (hf i)
+  exact setIntegral_mono_ae (hint i).integrableOn integrable_condexp.integrableOn (hf i)
 #align measure_theory.submartingale_nat MeasureTheory.submartingale_nat
 
 theorem supermartingale_nat [IsFiniteMeasure μ] {f : ℕ → Ω → ℝ} (hadp : Adapted 𝒢 f)

Fixes #11441.

@@ -82,7 +82,7 @@ theorem martingale_const_fun [OrderBot ι] (ℱ : Filtration ι m0) (μ : Measur
 variable (E)
 
 theorem martingale_zero (ℱ : Filtration ι m0) (μ : Measure Ω) : Martingale (0 : ι → Ω → E) ℱ μ :=
-  ⟨adapted_zero E ℱ, fun i j _ => by rw [Pi.zero_apply, condexp_zero]; simp; rfl⟩
+  ⟨adapted_zero E ℱ, fun i j _ => by rw [Pi.zero_apply, condexp_zero]; simp⟩
 #align measure_theory.martingale_zero MeasureTheory.martingale_zero
 
 variable {E}

After #9949, Pi.smul_apply can be used in simp again. This PR cleans up some workarounds.

@@ -129,7 +129,7 @@ theorem sub (hf : Martingale f ℱ μ) (hg : Martingale g ℱ μ) : Martingale (
 theorem smul (c : ℝ) (hf : Martingale f ℱ μ) : Martingale (c • f) ℱ μ := by
   refine' ⟨hf.adapted.smul c, fun i j hij => _⟩
   refine' (condexp_smul c (f j)).trans ((hf.2 i j hij).mono fun x hx => _)
-  rw [Pi.smul_apply, hx, Pi.smul_apply, Pi.smul_apply]
+  simp only [Pi.smul_apply, hx]
 #align measure_theory.martingale.smul MeasureTheory.Martingale.smul
 
 theorem supermartingale [Preorder E] (hf : Martingale f ℱ μ) : Supermartingale f ℱ μ :=

Remove the duplicates introduced in #8869 by sorting the lemmas in Algebra.Order.SMul into three files:

• Algebra.Order.Module.Defs for the order isomorphism induced by scalar multiplication by a positivity element
• Algebra.Order.Module.Pointwise for the order properties of scalar multiplication of sets. This file is new. I credit myself for https://github.com/leanprover-community/mathlib/pull/9078
• Algebra.Order.Module.OrderedSMul: The material about OrderedSMul per se. Inherits the copyright header from Algebra.Order.SMul. This file should eventually be deleted.

I move each #align to the correct file. On top of that, I delete unused redundant OrderedSMul instances (they were useful in Lean 3, but not anymore) and eq_of_smul_eq_smul_of_pos_of_le/eq_of_smul_eq_smul_of_neg_of_le since those lemmas are weird and unused.

@@ -353,7 +353,7 @@ theorem smul_nonneg {f : ι → Ω → F} {c : ℝ} (hc : 0 ≤ c) (hf : Superma
   refine' (condexp_smul c (f j)).le.trans _
   filter_upwards [hf.2.1 i j hij] with _ hle
   simp_rw [Pi.smul_apply]
-  exact smul_le_smul_of_nonneg hle hc
+  exact smul_le_smul_of_nonneg_left hle hc
 #align measure_theory.supermartingale.smul_nonneg MeasureTheory.Supermartingale.smul_nonneg
 
 theorem smul_nonpos {f : ι → Ω → F} {c : ℝ} (hc : c ≤ 0) (hf : Supermartingale f ℱ μ) :

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

This has nice performance benefits.

@@ -44,7 +44,7 @@ open scoped NNReal ENNReal MeasureTheory ProbabilityTheory BigOperators
 
 namespace MeasureTheory
 
-variable {Ω E ι : Type _} [Preorder ι] {m0 : MeasurableSpace Ω} {μ : Measure Ω}
+variable {Ω E ι : Type*} [Preorder ι] {m0 : MeasurableSpace Ω} {μ : Measure Ω}
   [NormedAddCommGroup E] [NormedSpace ℝ E] [CompleteSpace E] {f g : ι → Ω → E} {ℱ : Filtration ι m0}
 
 /-- A family of functions `f : ι → Ω → E` is a martingale with respect to a filtration `ℱ` if `f`
@@ -344,7 +344,7 @@ theorem sub_martingale [Preorder E] [CovariantClass E E (· + ·) (· ≤ ·)]
 
 section
 
-variable {F : Type _} [NormedLatticeAddCommGroup F] [NormedSpace ℝ F] [CompleteSpace F]
+variable {F : Type*} [NormedLatticeAddCommGroup F] [NormedSpace ℝ F] [CompleteSpace F]
   [OrderedSMul ℝ F]
 
 theorem smul_nonneg {f : ι → Ω → F} {c : ℝ} (hc : 0 ≤ c) (hf : Supermartingale f ℱ μ) :
@@ -370,7 +370,7 @@ namespace Submartingale
 
 section
 
-variable {F : Type _} [NormedLatticeAddCommGroup F] [NormedSpace ℝ F] [CompleteSpace F]
+variable {F : Type*} [NormedLatticeAddCommGroup F] [NormedSpace ℝ F] [CompleteSpace F]
   [OrderedSMul ℝ F]
 
 theorem smul_nonneg {f : ι → Ω → F} {c : ℝ} (hc : 0 ≤ c) (hf : Submartingale f ℱ μ) :

• 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) 2021 Rémy Degenne. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne, Kexing Ying
-
-! This file was ported from Lean 3 source module probability.martingale.basic
-! 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.Probability.Notation
 import Mathlib.Probability.Process.Stopping
 
+#align_import probability.martingale.basic from "leanprover-community/mathlib"@"ba074af83b6cf54c3104e59402b39410ddbd6dca"
+
 /-!
 # Martingales