measure_theory.integral.exp_decay | Mathlib porting status

Changes since the initial port

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

Changes in mathlib3

d4817f88

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

fd4551cf

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -49,7 +49,7 @@ theorem integrable_of_isBigO_exp_neg {f : ℝ → ℝ} {a b : ℝ} (h0 : 0 < b)
     (h1 : ContinuousOn f (Ici a)) (h2 : f =O[atTop] fun x => exp (-b * x)) :
     IntegrableOn f (Ioi a) := by
   cases' h2.is_O_with with c h3
-  rw [Asymptotics.isBigOWith_iff, eventually_at_top] at h3 
+  rw [Asymptotics.isBigOWith_iff, eventually_at_top] at h3
   cases' h3 with r bdr
   let v := max a r
   -- show integrable on `(a, v]` from continuity
@@ -72,7 +72,7 @@ theorem integrable_of_isBigO_exp_neg {f : ℝ → ℝ} {a b : ℝ} (h0 : 0 < b)
   refine' (ae_restrict_iff' measurableSet_Ioi).mpr _
   refine' ae_of_all _ fun x h1x => _
   rw [norm_mul, norm_eq_abs]
-  rw [mem_Ioi] at h1x 
+  rw [mem_Ioi] at h1x
   specialize bdr x ((le_max_right a r).trans h1x.le)
   exact bdr.trans (mul_le_mul_of_nonneg_right (le_abs_self c) (norm_nonneg _))
 #align integrable_of_is_O_exp_neg integrable_of_isBigO_exp_neg

fd4551cf

bump to nightly-2023-12-22-06

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

485b2c6c

Diff

@@ -55,7 +55,7 @@ theorem integrable_of_isBigO_exp_neg {f : ℝ → ℝ} {a b : ℝ} (h0 : 0 < b)
   -- show integrable on `(a, v]` from continuity
   have int_left : integrable_on f (Ioc a v) :=
     by
-    rw [← intervalIntegrable_iff_integrable_Ioc_of_le (le_max_left a r)]
+    rw [← intervalIntegrable_iff_integrableOn_Ioc_of_le (le_max_left a r)]
     have u : Icc a v ⊆ Ici a := Icc_subset_Ici_self
     exact (h1.mono u).intervalIntegrable_of_Icc (le_max_left a r)
   suffices integrable_on f (Ioi v)

fd4551cf

bump to nightly-2023-11-29-11

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

049e2cad

Diff

@@ -33,7 +33,7 @@ open scoped Topology
 theorem exp_neg_integrableOn_Ioi (a : ℝ) {b : ℝ} (h : 0 < b) :
     IntegrableOn (fun x : ℝ => exp (-b * x)) (Ioi a) :=
   by
-  have : tendsto (fun x => -exp (-b * x) / b) at_top (𝓝 (-0 / b)) :=
+  have : tendsto (fun x => -NormedSpace.exp (-b * x) / b) at_top (𝓝 (-0 / b)) :=
     by
     refine' tendsto.div_const (tendsto.neg _) _
     exact tendsto_exp_at_bot.comp (tendsto_id.neg_const_mul_at_top (Right.neg_neg_iff.2 h))
@@ -65,7 +65,8 @@ theorem integrable_of_isBigO_exp_neg {f : ℝ → ℝ} {a b : ℝ} (h0 : 0 < b)
   -- now show integrable on `(v, ∞)` from asymptotic
   constructor
   · exact (h1.mono <| Ioi_subset_Ici <| le_max_left a r).AEStronglyMeasurable measurableSet_Ioi
-  have : has_finite_integral (fun x : ℝ => c * exp (-b * x)) (volume.restrict (Ioi v)) :=
+  have :
+    has_finite_integral (fun x : ℝ => c * NormedSpace.exp (-b * x)) (volume.restrict (Ioi v)) :=
     (exp_neg_integrableOn_Ioi v h0).HasFiniteIntegral.const_mul c
   apply this.mono
   refine' (ae_restrict_iff' measurableSet_Ioi).mpr _

fd4551cf

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2022 David Loeffler. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: David Loeffler
 -/
-import Mathbin.MeasureTheory.Integral.IntervalIntegral
-import Mathbin.MeasureTheory.Integral.IntegralEqImproper
+import MeasureTheory.Integral.IntervalIntegral
+import MeasureTheory.Integral.IntegralEqImproper
 
 #align_import measure_theory.integral.exp_decay from "leanprover-community/mathlib"@"fd4551cfe4b7484b81c2c9ba3405edae27659676"

fd4551cf

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2022 David Loeffler. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: David Loeffler
-
-! This file was ported from Lean 3 source module measure_theory.integral.exp_decay
-! leanprover-community/mathlib commit fd4551cfe4b7484b81c2c9ba3405edae27659676
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Integral.IntervalIntegral
 import Mathbin.MeasureTheory.Integral.IntegralEqImproper
 
+#align_import measure_theory.integral.exp_decay from "leanprover-community/mathlib"@"fd4551cfe4b7484b81c2c9ba3405edae27659676"
+
 /-!
 # Integrals with exponential decay at ∞

fd4551cf

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -31,6 +31,7 @@ open Real intervalIntegral MeasureTheory Set Filter
 
 open scoped Topology
 
+#print exp_neg_integrableOn_Ioi /-
 /-- `exp (-b * x)` is integrable on `(a, ∞)`. -/
 theorem exp_neg_integrableOn_Ioi (a : ℝ) {b : ℝ} (h : 0 < b) :
     IntegrableOn (fun x : ℝ => exp (-b * x)) (Ioi a) :=
@@ -42,7 +43,9 @@ theorem exp_neg_integrableOn_Ioi (a : ℝ) {b : ℝ} (h : 0 < b) :
   refine' integrable_on_Ioi_deriv_of_nonneg' (fun x hx => _) (fun x hx => (exp_pos _).le) this
   simpa [h.ne'] using ((hasDerivAt_id x).const_mul b).neg.exp.neg.div_const b
 #align exp_neg_integrable_on_Ioi exp_neg_integrableOn_Ioi
+-/
 
+#print integrable_of_isBigO_exp_neg /-
 /-- If `f` is continuous on `[a, ∞)`, and is `O (exp (-b * x))` at `∞` for some `b > 0`, then
 `f` is integrable on `(a, ∞)`. -/
 theorem integrable_of_isBigO_exp_neg {f : ℝ → ℝ} {a b : ℝ} (h0 : 0 < b)
@@ -75,4 +78,5 @@ theorem integrable_of_isBigO_exp_neg {f : ℝ → ℝ} {a b : ℝ} (h0 : 0 < b)
   specialize bdr x ((le_max_right a r).trans h1x.le)
   exact bdr.trans (mul_le_mul_of_nonneg_right (le_abs_self c) (norm_nonneg _))
 #align integrable_of_is_O_exp_neg integrable_of_isBigO_exp_neg
+-/

fd4551cf

bump to nightly-2023-06-11-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/c471da714c044131b90c133701e51b877c246677

6960a941

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: David Loeffler
 
 ! This file was ported from Lean 3 source module measure_theory.integral.exp_decay
-! leanprover-community/mathlib commit d4817f8867c368d6c5571f7379b3888aaec1d95a
+! leanprover-community/mathlib commit fd4551cfe4b7484b81c2c9ba3405edae27659676
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.MeasureTheory.Integral.IntegralEqImproper
 /-!
 # Integrals with exponential decay at ∞
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 As easy special cases of general theorems in the library, we prove the following test
 for integrability:

d4817f88

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -46,7 +46,7 @@ theorem integrable_of_isBigO_exp_neg {f : ℝ → ℝ} {a b : ℝ} (h0 : 0 < b)
     (h1 : ContinuousOn f (Ici a)) (h2 : f =O[atTop] fun x => exp (-b * x)) :
     IntegrableOn f (Ioi a) := by
   cases' h2.is_O_with with c h3
-  rw [Asymptotics.isBigOWith_iff, eventually_at_top] at h3
+  rw [Asymptotics.isBigOWith_iff, eventually_at_top] at h3 
   cases' h3 with r bdr
   let v := max a r
   -- show integrable on `(a, v]` from continuity
@@ -68,7 +68,7 @@ theorem integrable_of_isBigO_exp_neg {f : ℝ → ℝ} {a b : ℝ} (h0 : 0 < b)
   refine' (ae_restrict_iff' measurableSet_Ioi).mpr _
   refine' ae_of_all _ fun x h1x => _
   rw [norm_mul, norm_eq_abs]
-  rw [mem_Ioi] at h1x
+  rw [mem_Ioi] at h1x 
   specialize bdr x ((le_max_right a r).trans h1x.le)
   exact bdr.trans (mul_le_mul_of_nonneg_right (le_abs_self c) (norm_nonneg _))
 #align integrable_of_is_O_exp_neg integrable_of_isBigO_exp_neg

d4817f88

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -26,7 +26,7 @@ noncomputable section
 
 open Real intervalIntegral MeasureTheory Set Filter
 
-open Topology
+open scoped Topology
 
 /-- `exp (-b * x)` is integrable on `(a, ∞)`. -/
 theorem exp_neg_integrableOn_Ioi (a : ℝ) {b : ℝ} (h : 0 < b) :

d4817f88

bump to nightly-2023-05-23-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

4d066d3b

Diff

@@ -61,7 +61,7 @@ theorem integrable_of_isBigO_exp_neg {f : ℝ → ℝ} {a b : ℝ} (h0 : 0 < b)
     simpa only [Ioc_union_Ioi_eq_Ioi, le_max_iff, le_refl, true_or_iff] using t
   -- now show integrable on `(v, ∞)` from asymptotic
   constructor
-  · exact (h1.mono <| Ioi_subset_Ici <| le_max_left a r).AeStronglyMeasurable measurableSet_Ioi
+  · exact (h1.mono <| Ioi_subset_Ici <| le_max_left a r).AEStronglyMeasurable measurableSet_Ioi
   have : has_finite_integral (fun x : ℝ => c * exp (-b * x)) (volume.restrict (Ioi v)) :=
     (exp_neg_integrableOn_Ioi v h0).HasFiniteIntegral.const_mul c
   apply this.mono

d4817f88

bump to nightly-2023-05-04-10

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

3d8894bd

Diff

@@ -29,7 +29,7 @@ open Real intervalIntegral MeasureTheory Set Filter
 open Topology
 
 /-- `exp (-b * x)` is integrable on `(a, ∞)`. -/
-theorem expNegIntegrableOnIoi (a : ℝ) {b : ℝ} (h : 0 < b) :
+theorem exp_neg_integrableOn_Ioi (a : ℝ) {b : ℝ} (h : 0 < b) :
     IntegrableOn (fun x : ℝ => exp (-b * x)) (Ioi a) :=
   by
   have : tendsto (fun x => -exp (-b * x) / b) at_top (𝓝 (-0 / b)) :=
@@ -38,13 +38,13 @@ theorem expNegIntegrableOnIoi (a : ℝ) {b : ℝ} (h : 0 < b) :
     exact tendsto_exp_at_bot.comp (tendsto_id.neg_const_mul_at_top (Right.neg_neg_iff.2 h))
   refine' integrable_on_Ioi_deriv_of_nonneg' (fun x hx => _) (fun x hx => (exp_pos _).le) this
   simpa [h.ne'] using ((hasDerivAt_id x).const_mul b).neg.exp.neg.div_const b
-#align exp_neg_integrable_on_Ioi expNegIntegrableOnIoi
+#align exp_neg_integrable_on_Ioi exp_neg_integrableOn_Ioi
 
 /-- If `f` is continuous on `[a, ∞)`, and is `O (exp (-b * x))` at `∞` for some `b > 0`, then
 `f` is integrable on `(a, ∞)`. -/
-theorem integrableOfIsOExpNeg {f : ℝ → ℝ} {a b : ℝ} (h0 : 0 < b) (h1 : ContinuousOn f (Ici a))
-    (h2 : f =O[atTop] fun x => exp (-b * x)) : IntegrableOn f (Ioi a) :=
-  by
+theorem integrable_of_isBigO_exp_neg {f : ℝ → ℝ} {a b : ℝ} (h0 : 0 < b)
+    (h1 : ContinuousOn f (Ici a)) (h2 : f =O[atTop] fun x => exp (-b * x)) :
+    IntegrableOn f (Ioi a) := by
   cases' h2.is_O_with with c h3
   rw [Asymptotics.isBigOWith_iff, eventually_at_top] at h3
   cases' h3 with r bdr
@@ -54,7 +54,7 @@ theorem integrableOfIsOExpNeg {f : ℝ → ℝ} {a b : ℝ} (h0 : 0 < b) (h1 : C
     by
     rw [← intervalIntegrable_iff_integrable_Ioc_of_le (le_max_left a r)]
     have u : Icc a v ⊆ Ici a := Icc_subset_Ici_self
-    exact (h1.mono u).intervalIntegrableOfIcc (le_max_left a r)
+    exact (h1.mono u).intervalIntegrable_of_Icc (le_max_left a r)
   suffices integrable_on f (Ioi v)
     by
     have t : integrable_on f (Ioc a v ∪ Ioi v) := integrable_on_union.mpr ⟨int_left, this⟩
@@ -63,7 +63,7 @@ theorem integrableOfIsOExpNeg {f : ℝ → ℝ} {a b : ℝ} (h0 : 0 < b) (h1 : C
   constructor
   · exact (h1.mono <| Ioi_subset_Ici <| le_max_left a r).AeStronglyMeasurable measurableSet_Ioi
   have : has_finite_integral (fun x : ℝ => c * exp (-b * x)) (volume.restrict (Ioi v)) :=
-    (expNegIntegrableOnIoi v h0).HasFiniteIntegral.const_mul c
+    (exp_neg_integrableOn_Ioi v h0).HasFiniteIntegral.const_mul c
   apply this.mono
   refine' (ae_restrict_iff' measurableSet_Ioi).mpr _
   refine' ae_of_all _ fun x h1x => _
@@ -71,5 +71,5 @@ theorem integrableOfIsOExpNeg {f : ℝ → ℝ} {a b : ℝ} (h0 : 0 < b) (h1 : C
   rw [mem_Ioi] at h1x
   specialize bdr x ((le_max_right a r).trans h1x.le)
   exact bdr.trans (mul_le_mul_of_nonneg_right (le_abs_self c) (norm_nonneg _))
-#align integrable_of_is_O_exp_neg integrableOfIsOExpNeg
+#align integrable_of_is_O_exp_neg integrable_of_isBigO_exp_neg

d4817f88

bump to nightly-2023-04-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e281deff072232a3c5b3e90034bd65dde396312

8c574543

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: David Loeffler
 
 ! This file was ported from Lean 3 source module measure_theory.integral.exp_decay
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit d4817f8867c368d6c5571f7379b3888aaec1d95a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -26,37 +26,18 @@ noncomputable section
 
 open Real intervalIntegral MeasureTheory Set Filter
 
-/-- Integral of `exp (-b * x)` over `(a, X)` is bounded as `X → ∞`. -/
-theorem integral_exp_neg_le {b : ℝ} (a X : ℝ) (h2 : 0 < b) :
-    (∫ x in a..X, exp (-b * x)) ≤ exp (-b * a) / b :=
-  by
-  rw [integral_deriv_eq_sub' fun x => -exp (-b * x) / b]
-  -- goal 1/4: F(X) - F(a) is bounded
-  · simp only [tsub_le_iff_right]
-    rw [neg_div b (exp (-b * a)), neg_div b (exp (-b * X)), add_neg_self, neg_le, neg_zero]
-    exact (div_pos (exp_pos _) h2).le
-  -- goal 2/4: the derivative of F is exp(-b x)
-  · ext1
-    simp [h2.ne']
-  -- goal 3/4: F is differentiable
-  · intro x hx
-    simp [h2.ne']
-  -- goal 4/4: exp(-b x) is continuous
-  · apply Continuous.continuousOn
-    continuity
-#align integral_exp_neg_le integral_exp_neg_le
+open Topology
 
 /-- `exp (-b * x)` is integrable on `(a, ∞)`. -/
 theorem expNegIntegrableOnIoi (a : ℝ) {b : ℝ} (h : 0 < b) :
     IntegrableOn (fun x : ℝ => exp (-b * x)) (Ioi a) :=
   by
-  have : ∀ X : ℝ, integrable_on (fun x : ℝ => exp (-b * x)) (Ioc a X) :=
+  have : tendsto (fun x => -exp (-b * x) / b) at_top (𝓝 (-0 / b)) :=
     by
-    intro X
-    exact (continuous_const.mul continuous_id).exp.integrableOnIoc
-  apply integrable_on_Ioi_of_interval_integral_norm_bounded (exp (-b * a) / b) a this tendsto_id
-  simp only [eventually_at_top, norm_of_nonneg (exp_pos _).le]
-  exact ⟨a, fun b2 hb2 => integral_exp_neg_le a b2 h⟩
+    refine' tendsto.div_const (tendsto.neg _) _
+    exact tendsto_exp_at_bot.comp (tendsto_id.neg_const_mul_at_top (Right.neg_neg_iff.2 h))
+  refine' integrable_on_Ioi_deriv_of_nonneg' (fun x hx => _) (fun x hx => (exp_pos _).le) this
+  simpa [h.ne'] using ((hasDerivAt_id x).const_mul b).neg.exp.neg.div_const b
 #align exp_neg_integrable_on_Ioi expNegIntegrableOnIoi
 
 /-- If `f` is continuous on `[a, ∞)`, and is `O (exp (-b * x))` at `∞` for some `b > 0`, then

70fd9563

bump to nightly-2023-04-12-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/039ef89bef6e58b32b62898dd48e9d1a4312bb65

0809e5be

Diff

@@ -65,7 +65,7 @@ theorem integrableOfIsOExpNeg {f : ℝ → ℝ} {a b : ℝ} (h0 : 0 < b) (h1 : C
     (h2 : f =O[atTop] fun x => exp (-b * x)) : IntegrableOn f (Ioi a) :=
   by
   cases' h2.is_O_with with c h3
-  rw [Asymptotics.isOWith_iff, eventually_at_top] at h3
+  rw [Asymptotics.isBigOWith_iff, eventually_at_top] at h3
   cases' h3 with r bdr
   let v := max a r
   -- show integrable on `(a, v]` from continuity

70fd9563

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

d4817f88

feat: bounding integrals by asymptotics, part 2: corollaries (#10388)

Shortcuts for linearly ordered domains and/or continuous functions. As an example, I golf the existing integrable_of_isBigO_exp_neg.

Another example usage: https://github.com/AlexKontorovich/PrimeNumberTheoremAnd/blob/1909a40253607bd2df18a738fc504fe81b132974/PrimeNumberTheoremAnd/PerronFormula.lean#L414-L436

Co-authored-by: L Lllvvuu <git@llllvvuu.dev>

434972cc

Diff

@@ -3,6 +3,7 @@ Copyright (c) 2022 David Loeffler. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: David Loeffler
 -/
+import Mathlib.MeasureTheory.Integral.Asymptotics
 import Mathlib.MeasureTheory.Integral.IntervalIntegral
 import Mathlib.MeasureTheory.Integral.IntegralEqImproper
 
@@ -38,31 +39,10 @@ theorem exp_neg_integrableOn_Ioi (a : ℝ) {b : ℝ} (h : 0 < b) :
 /-- If `f` is continuous on `[a, ∞)`, and is `O (exp (-b * x))` at `∞` for some `b > 0`, then
 `f` is integrable on `(a, ∞)`. -/
 theorem integrable_of_isBigO_exp_neg {f : ℝ → ℝ} {a b : ℝ} (h0 : 0 < b)
-    (h1 : ContinuousOn f (Ici a)) (h2 : f =O[atTop] fun x => exp (-b * x)) :
-    IntegrableOn f (Ioi a) := by
-  cases' h2.isBigOWith with c h3
-  rw [Asymptotics.isBigOWith_iff, eventually_atTop] at h3
-  cases' h3 with r bdr
-  let v := max a r
-  -- show integrable on `(a, v]` from continuity
-  have int_left : IntegrableOn f (Ioc a v) := by
-    rw [← intervalIntegrable_iff_integrableOn_Ioc_of_le (le_max_left a r)]
-    have u : Icc a v ⊆ Ici a := Icc_subset_Ici_self
-    exact (h1.mono u).intervalIntegrable_of_Icc (le_max_left a r)
-  suffices IntegrableOn f (Ioi v) by
-    have t := integrableOn_union.mpr ⟨int_left, this⟩
-    simpa only [v, Ioc_union_Ioi_eq_Ioi, le_max_iff, le_refl, true_or_iff] using t
-  -- now show integrable on `(v, ∞)` from asymptotic
-  constructor
-  · exact (h1.mono <| Ioi_subset_Ici <| le_max_left a r).aestronglyMeasurable measurableSet_Ioi
-  have : HasFiniteIntegral (fun x : ℝ => c * exp (-b * x)) (volume.restrict (Ioi v)) :=
-    (exp_neg_integrableOn_Ioi v h0).hasFiniteIntegral.const_mul c
-  apply this.mono
-  refine' (ae_restrict_iff' measurableSet_Ioi).mpr _
-  filter_upwards with x h1x
-  rw [norm_mul, norm_eq_abs]
-  rw [mem_Ioi] at h1x
-  specialize bdr x ((le_max_right a r).trans h1x.le)
-  exact bdr.trans (mul_le_mul_of_nonneg_right (le_abs_self c) (norm_nonneg _))
+    (hf : ContinuousOn f (Ici a)) (ho : f =O[atTop] fun x => exp (-b * x)) :
+    IntegrableOn f (Ioi a) :=
+  integrableOn_Ici_iff_integrableOn_Ioi.mp <|
+    (hf.locallyIntegrableOn measurableSet_Ici).integrableOn_of_isBigO_atTop
+    ho ⟨Ioi b, Ioi_mem_atTop b, exp_neg_integrableOn_Ioi b h0⟩
 set_option linter.uppercaseLean3 false in
 #align integrable_of_is_O_exp_neg integrable_of_isBigO_exp_neg

d4817f88

chore: golf using filter_upwards (#11208)

This is presumably not exhaustive, but covers about a hundred instances.

Style opinions (e.g., why a particular change is great/not a good idea) are very welcome; I'm still forming my own.

f637899e

Diff

@@ -59,7 +59,7 @@ theorem integrable_of_isBigO_exp_neg {f : ℝ → ℝ} {a b : ℝ} (h0 : 0 < b)
     (exp_neg_integrableOn_Ioi v h0).hasFiniteIntegral.const_mul c
   apply this.mono
   refine' (ae_restrict_iff' measurableSet_Ioi).mpr _
-  refine' ae_of_all _ fun x h1x => _
+  filter_upwards with x h1x
   rw [norm_mul, norm_eq_abs]
   rw [mem_Ioi] at h1x
   specialize bdr x ((le_max_right a r).trans h1x.le)

d4817f88

chore: more backporting of simp changes from #10995 (#11001)

Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

d9589c14

Diff

@@ -51,7 +51,7 @@ theorem integrable_of_isBigO_exp_neg {f : ℝ → ℝ} {a b : ℝ} (h0 : 0 < b)
     exact (h1.mono u).intervalIntegrable_of_Icc (le_max_left a r)
   suffices IntegrableOn f (Ioi v) by
     have t := integrableOn_union.mpr ⟨int_left, this⟩
-    simpa only [Ioc_union_Ioi_eq_Ioi, le_max_iff, le_refl, true_or_iff] using t
+    simpa only [v, Ioc_union_Ioi_eq_Ioi, le_max_iff, le_refl, true_or_iff] using t
   -- now show integrable on `(v, ∞)` from asymptotic
   constructor
   · exact (h1.mono <| Ioi_subset_Ici <| le_max_left a r).aestronglyMeasurable measurableSet_Ioi

d4817f88

feat: non-integrability results of derivatives on [a, +oo) (#8712)

We have in the library the lemma not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter, saying that if a function tends to infinity at a point in an interval [a, b], then its derivative is not interval-integrable on [a, b]. We generalize this result to allow for any set instead of [a, b], and apply it to half-infinite intervals.

In particular, we characterize integrability of x^s on [a, +oo), and deduce that x^s is never integrable on [0, +oo). This makes it possible to remove one assumption in Lemma mellin_comp_rpow on the Mellin transform.

051aa734

Diff

@@ -46,7 +46,7 @@ theorem integrable_of_isBigO_exp_neg {f : ℝ → ℝ} {a b : ℝ} (h0 : 0 < b)
   let v := max a r
   -- show integrable on `(a, v]` from continuity
   have int_left : IntegrableOn f (Ioc a v) := by
-    rw [← intervalIntegrable_iff_integrable_Ioc_of_le (le_max_left a r)]
+    rw [← intervalIntegrable_iff_integrableOn_Ioc_of_le (le_max_left a r)]
     have u : Icc a v ⊆ Ici a := Icc_subset_Ici_self
     exact (h1.mono u).intervalIntegrable_of_Icc (le_max_left a r)
   suffices IntegrableOn f (Ioi v) by

d4817f88

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2022 David Loeffler. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: David Loeffler
-
-! This file was ported from Lean 3 source module measure_theory.integral.exp_decay
-! leanprover-community/mathlib commit d4817f8867c368d6c5571f7379b3888aaec1d95a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.MeasureTheory.Integral.IntervalIntegral
 import Mathlib.MeasureTheory.Integral.IntegralEqImproper
 
+#align_import measure_theory.integral.exp_decay from "leanprover-community/mathlib"@"d4817f8867c368d6c5571f7379b3888aaec1d95a"
+
 /-!
 # Integrals with exponential decay at ∞

d4817f88

feat: port MeasureTheory.Integral.ExpDecay (#4905)

cc6a12ba

`measure_theory.integral.exp_decay` ⟷ `Mathlib.MeasureTheory.Integral.ExpDecay`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 1092

measure_theory.integral.exp_decay ⟷ Mathlib.MeasureTheory.Integral.ExpDecay

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 1092

`measure_theory.integral.exp_decay` ⟷ `Mathlib.MeasureTheory.Integral.ExpDecay`