analysis.special_functions.non_integrable ⟷ Mathlib.Analysis.SpecialFunctions.NonIntegrable

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

@@ -73,7 +73,7 @@ theorem not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter {f :
         ∀ y ∈ [x.1, x.2], (DifferentiableAt ℝ f y ∧ ‖deriv f y‖ ≤ C * ‖g y‖) ∧ y ∈ [a, b] :=
       (tendsto_fst.uIcc tendsto_snd).Eventually ((hd.and hC.bound).And hl).smallSets
     rcases mem_prod_self_iff.1 h with ⟨s, hsl, hs⟩
-    simp only [prod_subset_iff, mem_set_of_eq] at hs 
+    simp only [prod_subset_iff, mem_set_of_eq] at hs
     exact
       ⟨C, C₀, s, hsl, fun x hx y hy z hz => (hs x hx y hy z hz).2, fun x hx y hy z hz =>
         (hs x hx y hy z hz).1.1, fun x hx y hy z hz => (hs x hx y hy z hz).1.2⟩

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

@@ -181,7 +181,7 @@ theorem intervalIntegrable_sub_inv_iff {a b c : ℝ} :
     IntervalIntegrable (fun x => (x - c)⁻¹) volume a b ↔ a = b ∨ c ∉ [a, b] :=
   by
   constructor
-  · refine' fun h => or_iff_not_imp_left.2 fun hne hc => _
+  · refine' fun h => Classical.or_iff_not_imp_left.2 fun hne hc => _
     exact not_intervalIntegrable_of_sub_inv_isBigO_punctured (is_O_refl _ _) hne hc h
   · rintro (rfl | h₀)
     · exact IntervalIntegrable.refl

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
-import Mathbin.Analysis.SpecialFunctions.Log.Deriv
-import Mathbin.MeasureTheory.Integral.FundThmCalculus
+import Analysis.SpecialFunctions.Log.Deriv
+import MeasureTheory.Integral.FundThmCalculus
 
 #align_import analysis.special_functions.non_integrable from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.special_functions.non_integrable
-! leanprover-community/mathlib commit 6b31d1eebd64eab86d5bd9936bfaada6ca8b5842
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.SpecialFunctions.Log.Deriv
 import Mathbin.MeasureTheory.Integral.FundThmCalculus
 
+#align_import analysis.special_functions.non_integrable from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"
+
 /-!
 # Non integrable functions
 

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

@@ -52,6 +52,7 @@ open MeasureTheory TopologicalSpace Set Filter Asymptotics intervalIntegral
 variable {E F : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E] [SecondCountableTopology E]
   [CompleteSpace E] [NormedAddCommGroup F]
 
+#print not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter /-
 /-- If `f` is eventually differentiable along a nontrivial filter `l : filter ℝ` that is generated
 by convex sets, the norm of `f` tends to infinity along `l`, and `f' = O(g)` along `l`, where `f'`
 is the derivative of `f`, then `g` is not integrable on any interval `a..b` such that
@@ -106,7 +107,9 @@ theorem not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter {f :
       set_integral_mono_set hgi.def (ae_of_all _ fun x => mul_nonneg hC₀ (norm_nonneg _))
         hsub'.eventually_le
 #align not_interval_integrable_of_tendsto_norm_at_top_of_deriv_is_O_filter not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter
+-/
 
+#print not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_within_diff_singleton /-
 /-- If `a ≠ b`, `c ∈ [a, b]`, `f` is differentiable in the neighborhood of `c` within
 `[a, b] \ {c}`, `‖f x‖ → ∞` as `x → c` within `[a, b] \ {c}`, and `f' = O(g)` along
 `𝓝[[a, b] \ {c}] c`, where `f'` is the derivative of `f`, then `g` is not interval integrable on
@@ -134,7 +137,9 @@ theorem not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_within_diff
       (mem_of_superset hmem (diff_subset _ _)) (h_deriv.filter_mono this) (h_infty.mono_left this)
       (hg.mono this)
 #align not_interval_integrable_of_tendsto_norm_at_top_of_deriv_is_O_within_diff_singleton not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_within_diff_singleton
+-/
 
+#print not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_punctured /-
 /-- If `f` is differentiable in a punctured neighborhood of `c`, `‖f x‖ → ∞` as `x → c` (more
 formally, along the filter `𝓝[≠] c`), and `f' = O(g)` along `𝓝[≠] c`, where `f'` is the derivative
 of `f`, then `g` is not interval integrable on any nontrivial interval `a..b` such that
@@ -147,7 +152,9 @@ theorem not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_punctured {
   not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_within_diff_singleton hne hc
     (h_deriv.filter_mono this) (h_infty.mono_left this) (hg.mono this)
 #align not_interval_integrable_of_tendsto_norm_at_top_of_deriv_is_O_punctured not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_punctured
+-/
 
+#print not_intervalIntegrable_of_sub_inv_isBigO_punctured /-
 /-- If `f` grows in the punctured neighborhood of `c : ℝ` at least as fast as `1 / (x - c)`,
 then it is not interval integrable on any nontrivial interval `a..b`, `c ∈ [a, b]`. -/
 theorem not_intervalIntegrable_of_sub_inv_isBigO_punctured {f : ℝ → F} {a b c : ℝ}
@@ -168,6 +175,7 @@ theorem not_intervalIntegrable_of_sub_inv_isBigO_punctured {f : ℝ → F} {a b
       (A.mono fun x hx => hx.DifferentiableAt) B
       (hf.congr' (A.mono fun x hx => hx.deriv.symm) eventually_eq.rfl) hne hc
 #align not_interval_integrable_of_sub_inv_is_O_punctured not_intervalIntegrable_of_sub_inv_isBigO_punctured
+-/
 
 #print intervalIntegrable_sub_inv_iff /-
 /-- The function `λ x, (x - c)⁻¹` is integrable on `a..b` if and only if `a = b` or `c ∉ [a, b]`. -/

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

@@ -80,10 +80,10 @@ theorem not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter {f :
       ⟨C, C₀, s, hsl, fun x hx y hy z hz => (hs x hx y hy z hz).2, fun x hx y hy z hz =>
         (hs x hx y hy z hz).1.1, fun x hx y hy z hz => (hs x hx y hy z hz).1.2⟩
   replace hgi : IntervalIntegrable (fun x => C * ‖g x‖) volume a b; · convert hgi.norm.smul C
-  obtain ⟨c, hc, d, hd, hlt⟩ : ∃ c ∈ s, ∃ d ∈ s, (‖f c‖ + ∫ y in Ι a b, C * ‖g y‖) < ‖f d‖ :=
+  obtain ⟨c, hc, d, hd, hlt⟩ : ∃ c ∈ s, ∃ d ∈ s, ‖f c‖ + ∫ y in Ι a b, C * ‖g y‖ < ‖f d‖ :=
     by
     rcases Filter.nonempty_of_mem hsl with ⟨c, hc⟩
-    have : ∀ᶠ x in l, (‖f c‖ + ∫ y in Ι a b, C * ‖g y‖) < ‖f x‖ :=
+    have : ∀ᶠ x in l, ‖f c‖ + ∫ y in Ι a b, C * ‖g y‖ < ‖f x‖ :=
       hf.eventually (eventually_gt_at_top _)
     exact ⟨c, hc, (this.and hsl).exists.imp fun d hd => ⟨hd.2, hd.1⟩⟩
   specialize hsub c hc d hd; specialize hfd c hc d hd

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: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module analysis.special_functions.non_integrable
-! leanprover-community/mathlib commit 55ec6e9af7d3e0043f57e394cb06a72f6275273e
+! leanprover-community/mathlib commit 6b31d1eebd64eab86d5bd9936bfaada6ca8b5842
 ! 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.FundThmCalculus
 /-!
 # Non integrable functions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove that the derivative of a function that tends to infinity is not interval
 integrable, see `interval_integral.not_integrable_has_deriv_at_of_tendsto_norm_at_top_filter` and
 `interval_integral.not_integrable_has_deriv_at_of_tendsto_norm_at_top_punctured`.  Then we apply the

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

@@ -102,7 +102,6 @@ theorem not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter {f :
     _ ≤ ∫ x in Ι a b, C * ‖g x‖ :=
       set_integral_mono_set hgi.def (ae_of_all _ fun x => mul_nonneg hC₀ (norm_nonneg _))
         hsub'.eventually_le
-    
 #align not_interval_integrable_of_tendsto_norm_at_top_of_deriv_is_O_filter not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter
 
 /-- If `a ≠ b`, `c ∈ [a, b]`, `f` is differentiable in the neighborhood of `c` within

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

@@ -167,6 +167,7 @@ theorem not_intervalIntegrable_of_sub_inv_isBigO_punctured {f : ℝ → F} {a b
       (hf.congr' (A.mono fun x hx => hx.deriv.symm) eventually_eq.rfl) hne hc
 #align not_interval_integrable_of_sub_inv_is_O_punctured not_intervalIntegrable_of_sub_inv_isBigO_punctured
 
+#print intervalIntegrable_sub_inv_iff /-
 /-- The function `λ x, (x - c)⁻¹` is integrable on `a..b` if and only if `a = b` or `c ∉ [a, b]`. -/
 @[simp]
 theorem intervalIntegrable_sub_inv_iff {a b c : ℝ} :
@@ -180,11 +181,14 @@ theorem intervalIntegrable_sub_inv_iff {a b c : ℝ} :
     refine' ((continuous_sub_right c).ContinuousOn.inv₀ _).IntervalIntegrable
     exact fun x hx => sub_ne_zero.2 <| ne_of_mem_of_not_mem hx h₀
 #align interval_integrable_sub_inv_iff intervalIntegrable_sub_inv_iff
+-/
 
+#print intervalIntegrable_inv_iff /-
 /-- The function `λ x, x⁻¹` is integrable on `a..b` if and only if `a = b` or `0 ∉ [a, b]`. -/
 @[simp]
 theorem intervalIntegrable_inv_iff {a b : ℝ} :
     IntervalIntegrable (fun x => x⁻¹) volume a b ↔ a = b ∨ (0 : ℝ) ∉ [a, b] := by
   simp only [← intervalIntegrable_sub_inv_iff, sub_zero]
 #align interval_integrable_inv_iff intervalIntegrable_inv_iff
+-/
 

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

@@ -154,7 +154,7 @@ theorem not_intervalIntegrable_of_sub_inv_isBigO_punctured {f : ℝ → F} {a b
   by
   have A : ∀ᶠ x in 𝓝[≠] c, HasDerivAt (fun x => Real.log (x - c)) (x - c)⁻¹ x :=
     by
-    filter_upwards [self_mem_nhdsWithin]with x hx
+    filter_upwards [self_mem_nhdsWithin] with x hx
     simpa using ((hasDerivAt_id x).sub_const c).log (sub_ne_zero.2 hx)
   have B : tendsto (fun x => ‖Real.log (x - c)‖) (𝓝[≠] c) at_top :=
     by

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

@@ -60,7 +60,7 @@ theorem not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter {f :
   by
   intro hgi
   obtain ⟨C, hC₀, s, hsl, hsub, hfd, hg⟩ :
-    ∃ (C : ℝ)(hC₀ : 0 ≤ C),
+    ∃ (C : ℝ) (hC₀ : 0 ≤ C),
       ∃ s ∈ l,
         (∀ x ∈ s, ∀ y ∈ s, [x, y] ⊆ [a, b]) ∧
           (∀ x ∈ s, ∀ y ∈ s, ∀ z ∈ [x, y], DifferentiableAt ℝ f z) ∧
@@ -72,7 +72,7 @@ theorem not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter {f :
         ∀ y ∈ [x.1, x.2], (DifferentiableAt ℝ f y ∧ ‖deriv f y‖ ≤ C * ‖g y‖) ∧ y ∈ [a, b] :=
       (tendsto_fst.uIcc tendsto_snd).Eventually ((hd.and hC.bound).And hl).smallSets
     rcases mem_prod_self_iff.1 h with ⟨s, hsl, hs⟩
-    simp only [prod_subset_iff, mem_set_of_eq] at hs
+    simp only [prod_subset_iff, mem_set_of_eq] at hs 
     exact
       ⟨C, C₀, s, hsl, fun x hx y hy z hz => (hs x hx y hy z hz).2, fun x hx y hy z hz =>
         (hs x hx y hy z hz).1.1, fun x hx y hy z hz => (hs x hx y hy z hz).1.2⟩

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

@@ -90,7 +90,7 @@ theorem not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter {f :
     (ae_restrict_mem measurableSet_uIoc).mono hg
   have hsub' : Ι c d ⊆ Ι a b := uIoc_subset_uIoc_of_uIcc_subset_uIcc hsub
   have hfi : IntervalIntegrable (deriv f) volume c d :=
-    (hgi.mono_set hsub).mono_fun' (aEStronglyMeasurable_deriv _ _) hg_ae
+    (hgi.mono_set hsub).mono_fun' (aestronglyMeasurable_deriv _ _) hg_ae
   refine' hlt.not_le (sub_le_iff_le_add'.1 _)
   calc
     ‖f d‖ - ‖f c‖ ≤ ‖f d - f c‖ := norm_sub_norm_le _ _

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

@@ -42,7 +42,7 @@ integrable function
 -/
 
 
-open MeasureTheory Topology Interval NNReal ENNReal
+open scoped MeasureTheory Topology Interval NNReal ENNReal
 
 open MeasureTheory TopologicalSpace Set Filter Asymptotics intervalIntegral
 

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

@@ -76,17 +76,15 @@ theorem not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter {f :
     exact
       ⟨C, C₀, s, hsl, fun x hx y hy z hz => (hs x hx y hy z hz).2, fun x hx y hy z hz =>
         (hs x hx y hy z hz).1.1, fun x hx y hy z hz => (hs x hx y hy z hz).1.2⟩
-  replace hgi : IntervalIntegrable (fun x => C * ‖g x‖) volume a b
-  · convert hgi.norm.smul C
+  replace hgi : IntervalIntegrable (fun x => C * ‖g x‖) volume a b; · convert hgi.norm.smul C
   obtain ⟨c, hc, d, hd, hlt⟩ : ∃ c ∈ s, ∃ d ∈ s, (‖f c‖ + ∫ y in Ι a b, C * ‖g y‖) < ‖f d‖ :=
     by
     rcases Filter.nonempty_of_mem hsl with ⟨c, hc⟩
     have : ∀ᶠ x in l, (‖f c‖ + ∫ y in Ι a b, C * ‖g y‖) < ‖f x‖ :=
       hf.eventually (eventually_gt_at_top _)
     exact ⟨c, hc, (this.and hsl).exists.imp fun d hd => ⟨hd.2, hd.1⟩⟩
-  specialize hsub c hc d hd
-  specialize hfd c hc d hd
-  replace hg : ∀ x ∈ Ι c d, ‖deriv f x‖ ≤ C * ‖g x‖
+  specialize hsub c hc d hd; specialize hfd c hc d hd
+  replace hg : ∀ x ∈ Ι c d, ‖deriv f x‖ ≤ C * ‖g x‖;
   exact fun z hz => hg c hc d hd z ⟨hz.1.le, hz.2⟩
   have hg_ae : ∀ᵐ x ∂volume.restrict (Ι c d), ‖deriv f x‖ ≤ C * ‖g x‖ :=
     (ae_restrict_mem measurableSet_uIoc).mono hg

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

@@ -92,7 +92,7 @@ theorem not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter {f :
     (ae_restrict_mem measurableSet_uIoc).mono hg
   have hsub' : Ι c d ⊆ Ι a b := uIoc_subset_uIoc_of_uIcc_subset_uIcc hsub
   have hfi : IntervalIntegrable (deriv f) volume c d :=
-    (hgi.mono_set hsub).mono_fun' (aeStronglyMeasurable_deriv _ _) hg_ae
+    (hgi.mono_set hsub).mono_fun' (aEStronglyMeasurable_deriv _ _) hg_ae
   refine' hlt.not_le (sub_le_iff_le_add'.1 _)
   calc
     ‖f d‖ - ‖f c‖ ≤ ‖f d - f c‖ := norm_sub_norm_le _ _

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

@@ -4,11 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module analysis.special_functions.non_integrable
-! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
+! leanprover-community/mathlib commit 55ec6e9af7d3e0043f57e394cb06a72f6275273e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.Analysis.SpecialFunctions.Integrals
+import Mathbin.Analysis.SpecialFunctions.Log.Deriv
+import Mathbin.MeasureTheory.Integral.FundThmCalculus
 
 /-!
 # Non integrable functions
@@ -177,9 +178,9 @@ theorem intervalIntegrable_sub_inv_iff {a b c : ℝ} :
   · refine' fun h => or_iff_not_imp_left.2 fun hne hc => _
     exact not_intervalIntegrable_of_sub_inv_isBigO_punctured (is_O_refl _ _) hne hc h
   · rintro (rfl | h₀)
-    exacts[IntervalIntegrable.refl,
-      interval_integrable_inv (fun x hx => sub_ne_zero.2 <| ne_of_mem_of_not_mem hx h₀)
-        (continuous_on_id.sub continuousOn_const)]
+    · exact IntervalIntegrable.refl
+    refine' ((continuous_sub_right c).ContinuousOn.inv₀ _).IntervalIntegrable
+    exact fun x hx => sub_ne_zero.2 <| ne_of_mem_of_not_mem hx h₀
 #align interval_integrable_sub_inv_iff intervalIntegrable_sub_inv_iff
 
 /-- The function `λ x, x⁻¹` is integrable on `a..b` if and only if `a = b` or `0 ∉ [a, b]`. -/

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

@@ -91,7 +91,7 @@ theorem not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter {f :
     (ae_restrict_mem measurableSet_uIoc).mono hg
   have hsub' : Ι c d ⊆ Ι a b := uIoc_subset_uIoc_of_uIcc_subset_uIcc hsub
   have hfi : IntervalIntegrable (deriv f) volume c d :=
-    (hgi.mono_set hsub).monoFun' (aeStronglyMeasurableDeriv _ _) hg_ae
+    (hgi.mono_set hsub).mono_fun' (aeStronglyMeasurable_deriv _ _) hg_ae
   refine' hlt.not_le (sub_le_iff_le_add'.1 _)
   calc
     ‖f d‖ - ‖f c‖ ≤ ‖f d - f c‖ := norm_sub_norm_le _ _

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

@@ -4,12 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module analysis.special_functions.non_integrable
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.SpecialFunctions.Integrals
-import Mathbin.Analysis.Calculus.FderivMeasurable
 
 /-!
 # Non integrable functions

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

@@ -53,7 +53,7 @@ variable {E F : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E] [SecondCounta
 by convex sets, the norm of `f` tends to infinity along `l`, and `f' = O(g)` along `l`, where `f'`
 is the derivative of `f`, then `g` is not integrable on any interval `a..b` such that
 `[a, b] ∈ l`. -/
-theorem not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isO_filter {f : ℝ → E} {g : ℝ → F}
+theorem not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter {f : ℝ → E} {g : ℝ → F}
     {a b : ℝ} (l : Filter ℝ) [NeBot l] [TendstoIxxClass Icc l l] (hl : [a, b] ∈ l)
     (hd : ∀ᶠ x in l, DifferentiableAt ℝ f x) (hf : Tendsto (fun x => ‖f x‖) l atTop)
     (hfg : deriv f =O[l] g) : ¬IntervalIntegrable g volume a b :=
@@ -105,14 +105,14 @@ theorem not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isO_filter {f : 
       set_integral_mono_set hgi.def (ae_of_all _ fun x => mul_nonneg hC₀ (norm_nonneg _))
         hsub'.eventually_le
     
-#align not_interval_integrable_of_tendsto_norm_at_top_of_deriv_is_O_filter not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isO_filter
+#align not_interval_integrable_of_tendsto_norm_at_top_of_deriv_is_O_filter not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter
 
 /-- If `a ≠ b`, `c ∈ [a, b]`, `f` is differentiable in the neighborhood of `c` within
 `[a, b] \ {c}`, `‖f x‖ → ∞` as `x → c` within `[a, b] \ {c}`, and `f' = O(g)` along
 `𝓝[[a, b] \ {c}] c`, where `f'` is the derivative of `f`, then `g` is not interval integrable on
 `a..b`. -/
-theorem not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isO_within_diff_singleton {f : ℝ → E}
-    {g : ℝ → F} {a b c : ℝ} (hne : a ≠ b) (hc : c ∈ [a, b])
+theorem not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_within_diff_singleton
+    {f : ℝ → E} {g : ℝ → F} {a b c : ℝ} (hne : a ≠ b) (hc : c ∈ [a, b])
     (h_deriv : ∀ᶠ x in 𝓝[[a, b] \ {c}] c, DifferentiableAt ℝ f x)
     (h_infty : Tendsto (fun x => ‖f x‖) (𝓝[[a, b] \ {c}] c) atTop)
     (hg : deriv f =O[𝓝[[a, b] \ {c}] c] g) : ¬IntervalIntegrable g volume a b :=
@@ -130,27 +130,27 @@ theorem not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isO_within_diff_si
   skip
   have : l ≤ 𝓝[[a, b] \ {c}] c := le_inf hle (le_principal_iff.2 hmem)
   exact
-    not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isO_filter l
+    not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter l
       (mem_of_superset hmem (diff_subset _ _)) (h_deriv.filter_mono this) (h_infty.mono_left this)
       (hg.mono this)
-#align not_interval_integrable_of_tendsto_norm_at_top_of_deriv_is_O_within_diff_singleton not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isO_within_diff_singleton
+#align not_interval_integrable_of_tendsto_norm_at_top_of_deriv_is_O_within_diff_singleton not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_within_diff_singleton
 
 /-- If `f` is differentiable in a punctured neighborhood of `c`, `‖f x‖ → ∞` as `x → c` (more
 formally, along the filter `𝓝[≠] c`), and `f' = O(g)` along `𝓝[≠] c`, where `f'` is the derivative
 of `f`, then `g` is not interval integrable on any nontrivial interval `a..b` such that
 `c ∈ [a, b]`. -/
-theorem not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isO_punctured {f : ℝ → E} {g : ℝ → F}
-    {a b c : ℝ} (h_deriv : ∀ᶠ x in 𝓝[≠] c, DifferentiableAt ℝ f x)
+theorem not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_punctured {f : ℝ → E}
+    {g : ℝ → F} {a b c : ℝ} (h_deriv : ∀ᶠ x in 𝓝[≠] c, DifferentiableAt ℝ f x)
     (h_infty : Tendsto (fun x => ‖f x‖) (𝓝[≠] c) atTop) (hg : deriv f =O[𝓝[≠] c] g) (hne : a ≠ b)
     (hc : c ∈ [a, b]) : ¬IntervalIntegrable g volume a b :=
   have : 𝓝[[a, b] \ {c}] c ≤ 𝓝[≠] c := nhdsWithin_mono _ (inter_subset_right _ _)
-  not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isO_within_diff_singleton hne hc
+  not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_within_diff_singleton hne hc
     (h_deriv.filter_mono this) (h_infty.mono_left this) (hg.mono this)
-#align not_interval_integrable_of_tendsto_norm_at_top_of_deriv_is_O_punctured not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isO_punctured
+#align not_interval_integrable_of_tendsto_norm_at_top_of_deriv_is_O_punctured not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_punctured
 
 /-- If `f` grows in the punctured neighborhood of `c : ℝ` at least as fast as `1 / (x - c)`,
 then it is not interval integrable on any nontrivial interval `a..b`, `c ∈ [a, b]`. -/
-theorem not_intervalIntegrable_of_sub_inv_isO_punctured {f : ℝ → F} {a b c : ℝ}
+theorem not_intervalIntegrable_of_sub_inv_isBigO_punctured {f : ℝ → F} {a b c : ℝ}
     (hf : (fun x => (x - c)⁻¹) =O[𝓝[≠] c] f) (hne : a ≠ b) (hc : c ∈ [a, b]) :
     ¬IntervalIntegrable f volume a b :=
   by
@@ -164,10 +164,10 @@ theorem not_intervalIntegrable_of_sub_inv_isO_punctured {f : ℝ → F} {a b c :
     rw [← sub_self c]
     exact ((hasDerivAt_id c).sub_const c).tendsto_punctured_nhds one_ne_zero
   exact
-    not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isO_punctured
+    not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_punctured
       (A.mono fun x hx => hx.DifferentiableAt) B
       (hf.congr' (A.mono fun x hx => hx.deriv.symm) eventually_eq.rfl) hne hc
-#align not_interval_integrable_of_sub_inv_is_O_punctured not_intervalIntegrable_of_sub_inv_isO_punctured
+#align not_interval_integrable_of_sub_inv_is_O_punctured not_intervalIntegrable_of_sub_inv_isBigO_punctured
 
 /-- The function `λ x, (x - c)⁻¹` is integrable on `a..b` if and only if `a = b` or `c ∉ [a, b]`. -/
 @[simp]
@@ -176,7 +176,7 @@ theorem intervalIntegrable_sub_inv_iff {a b c : ℝ} :
   by
   constructor
   · refine' fun h => or_iff_not_imp_left.2 fun hne hc => _
-    exact not_intervalIntegrable_of_sub_inv_isO_punctured (is_O_refl _ _) hne hc h
+    exact not_intervalIntegrable_of_sub_inv_isBigO_punctured (is_O_refl _ _) hne hc h
   · rintro (rfl | h₀)
     exacts[IntervalIntegrable.refl,
       interval_integrable_inv (fun x hx => sub_ne_zero.2 <| ne_of_mem_of_not_mem hx h₀)

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -96,11 +96,11 @@ theorem not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isO_filter {f : 
   refine' hlt.not_le (sub_le_iff_le_add'.1 _)
   calc
     ‖f d‖ - ‖f c‖ ≤ ‖f d - f c‖ := norm_sub_norm_le _ _
-    _ = ‖∫ x in c..d, deriv f x‖ := congr_arg _ (integral_deriv_eq_sub hfd hfi).symm
-    _ = ‖∫ x in Ι c d, deriv f x‖ := norm_integral_eq_norm_integral_Ioc _
-    _ ≤ ∫ x in Ι c d, ‖deriv f x‖ := norm_integral_le_integral_norm _
+    _ = ‖∫ x in c..d, deriv f x‖ := (congr_arg _ (integral_deriv_eq_sub hfd hfi).symm)
+    _ = ‖∫ x in Ι c d, deriv f x‖ := (norm_integral_eq_norm_integral_Ioc _)
+    _ ≤ ∫ x in Ι c d, ‖deriv f x‖ := (norm_integral_le_integral_norm _)
     _ ≤ ∫ x in Ι c d, C * ‖g x‖ :=
-      set_integral_mono_on hfi.norm.def (hgi.def.mono_set hsub') measurableSet_uIoc hg
+      (set_integral_mono_on hfi.norm.def (hgi.def.mono_set hsub') measurableSet_uIoc hg)
     _ ≤ ∫ x in Ι a b, C * ‖g x‖ :=
       set_integral_mono_set hgi.def (ae_of_all _ fun x => mul_nonneg hC₀ (norm_nonneg _))
         hsub'.eventually_le

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

@@ -42,7 +42,7 @@ integrable function
 -/
 
 
-open MeasureTheory Topology Interval NNReal Ennreal
+open MeasureTheory Topology Interval NNReal ENNReal
 
 open MeasureTheory TopologicalSpace Set Filter Asymptotics intervalIntegral
 

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.

@@ -90,9 +90,9 @@ theorem not_integrableOn_of_tendsto_norm_atTop_of_deriv_isBigO_filter_aux
     _ = ‖∫ x in Ι c d, deriv f x‖ := norm_integral_eq_norm_integral_Ioc _
     _ ≤ ∫ x in Ι c d, ‖deriv f x‖ := norm_integral_le_integral_norm _
     _ ≤ ∫ x in Ι c d, C * ‖g x‖ :=
-      set_integral_mono_on hfi.norm.def' (hgi.mono_set hsub') measurableSet_uIoc hg
+      setIntegral_mono_on hfi.norm.def' (hgi.mono_set hsub') measurableSet_uIoc hg
     _ ≤ ∫ x in k, C * ‖g x‖ := by
-      apply set_integral_mono_set hgi
+      apply setIntegral_mono_set hgi
         (ae_of_all _ fun x => mul_nonneg hC₀ (norm_nonneg _)) hsub'.eventuallyLE
 
 theorem not_integrableOn_of_tendsto_norm_atTop_of_deriv_isBigO_filter

This will become an error in 2024-03-16 nightly, possibly not permanently.

Co-authored-by: Scott Morrison <scott@tqft.net>

@@ -90,7 +90,7 @@ theorem not_integrableOn_of_tendsto_norm_atTop_of_deriv_isBigO_filter_aux
     _ = ‖∫ x in Ι c d, deriv f x‖ := norm_integral_eq_norm_integral_Ioc _
     _ ≤ ∫ x in Ι c d, ‖deriv f x‖ := norm_integral_le_integral_norm _
     _ ≤ ∫ x in Ι c d, C * ‖g x‖ :=
-      set_integral_mono_on hfi.norm.def (hgi.mono_set hsub') measurableSet_uIoc hg
+      set_integral_mono_on hfi.norm.def' (hgi.mono_set hsub') measurableSet_uIoc hg
     _ ≤ ∫ x in k, C * ‖g x‖ := by
       apply set_integral_mono_set hgi
         (ae_of_all _ fun x => mul_nonneg hC₀ (norm_nonneg _)) hsub'.eventuallyLE

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -104,7 +104,7 @@ theorem not_integrableOn_of_tendsto_norm_atTop_of_deriv_isBigO_filter
   let f' := a ∘ f
   have h'd : ∀ᶠ x in l, DifferentiableAt ℝ f' x := by
     filter_upwards [hd] with x hx using a.toContinuousLinearMap.differentiableAt.comp x hx
-  have h'f : Tendsto (fun x => ‖f' x‖) l atTop := hf.congr (fun x ↦ by simp)
+  have h'f : Tendsto (fun x => ‖f' x‖) l atTop := hf.congr (fun x ↦ by simp [f'])
   have h'fg : deriv f' =O[l] g := by
     apply IsBigO.trans _ hfg
     rw [← isBigO_norm_norm]

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.

@@ -43,56 +43,93 @@ open scoped MeasureTheory Topology Interval NNReal ENNReal
 
 open MeasureTheory TopologicalSpace Set Filter Asymptotics intervalIntegral
 
-variable {E F : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] [SecondCountableTopology E]
-  [CompleteSpace E] [NormedAddCommGroup F]
+variable {E F : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] [NormedAddCommGroup F]
 
 /-- If `f` is eventually differentiable along a nontrivial filter `l : Filter ℝ` that is generated
 by convex sets, the norm of `f` tends to infinity along `l`, and `f' = O(g)` along `l`, where `f'`
-is the derivative of `f`, then `g` is not integrable on any interval `a..b` such that
-`[a, b] ∈ l`. -/
-theorem not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter {f : ℝ → E} {g : ℝ → F}
-    {a b : ℝ} (l : Filter ℝ) [NeBot l] [TendstoIxxClass Icc l l] (hl : [[a, b]] ∈ l)
-    (hd : ∀ᶠ x in l, DifferentiableAt ℝ f x) (hf : Tendsto (fun x => ‖f x‖) l atTop)
-    (hfg : deriv f =O[l] g) : ¬IntervalIntegrable g volume a b := by
+is the derivative of `f`, then `g` is not integrable on any set `k` belonging to `l`.
+Auxiliary version assuming that `E` is complete. -/
+theorem not_integrableOn_of_tendsto_norm_atTop_of_deriv_isBigO_filter_aux
+    [CompleteSpace E] {f : ℝ → E} {g : ℝ → F}
+    {k : Set ℝ} (l : Filter ℝ) [NeBot l] [TendstoIxxClass Icc l l]
+    (hl : k ∈ l) (hd : ∀ᶠ x in l, DifferentiableAt ℝ f x) (hf : Tendsto (fun x => ‖f x‖) l atTop)
+    (hfg : deriv f =O[l] g) : ¬IntegrableOn g k := by
   intro hgi
   obtain ⟨C, hC₀, s, hsl, hsub, hfd, hg⟩ :
-    ∃ (C : ℝ) (_ : 0 ≤ C), ∃ s ∈ l, (∀ x ∈ s, ∀ y ∈ s, [[x, y]] ⊆ [[a, b]]) ∧
+    ∃ (C : ℝ) (_ : 0 ≤ C), ∃ s ∈ l, (∀ x ∈ s, ∀ y ∈ s, [[x, y]] ⊆ k) ∧
       (∀ x ∈ s, ∀ y ∈ s, ∀ z ∈ [[x, y]], DifferentiableAt ℝ f z) ∧
         ∀ x ∈ s, ∀ y ∈ s, ∀ z ∈ [[x, y]], ‖deriv f z‖ ≤ C * ‖g z‖ := by
     rcases hfg.exists_nonneg with ⟨C, C₀, hC⟩
     have h : ∀ᶠ x : ℝ × ℝ in l.prod l,
-        ∀ y ∈ [[x.1, x.2]], (DifferentiableAt ℝ f y ∧ ‖deriv f y‖ ≤ C * ‖g y‖) ∧ y ∈ [[a, b]] :=
+        ∀ y ∈ [[x.1, x.2]], (DifferentiableAt ℝ f y ∧ ‖deriv f y‖ ≤ C * ‖g y‖) ∧ y ∈ k :=
       (tendsto_fst.uIcc tendsto_snd).eventually ((hd.and hC.bound).and hl).smallSets
     rcases mem_prod_self_iff.1 h with ⟨s, hsl, hs⟩
     simp only [prod_subset_iff, mem_setOf_eq] at hs
     exact ⟨C, C₀, s, hsl, fun x hx y hy z hz => (hs x hx y hy z hz).2, fun x hx y hy z hz =>
       (hs x hx y hy z hz).1.1, fun x hx y hy z hz => (hs x hx y hy z hz).1.2⟩
-  replace hgi : IntervalIntegrable (fun x => C * ‖g x‖) volume a b
-  · convert hgi.norm.smul C using 1
-  obtain ⟨c, hc, d, hd, hlt⟩ : ∃ c ∈ s, ∃ d ∈ s, (‖f c‖ + ∫ y in Ι a b, C * ‖g y‖) < ‖f d‖ := by
+  replace hgi : IntegrableOn (fun x ↦ C * ‖g x‖) k := by exact hgi.norm.smul C
+  obtain ⟨c, hc, d, hd, hlt⟩ : ∃ c ∈ s, ∃ d ∈ s, (‖f c‖ + ∫ y in k, C * ‖g y‖) < ‖f d‖ := by
     rcases Filter.nonempty_of_mem hsl with ⟨c, hc⟩
-    have : ∀ᶠ x in l, (‖f c‖ + ∫ y in Ι a b, C * ‖g y‖) < ‖f x‖ :=
+    have : ∀ᶠ x in l, (‖f c‖ + ∫ y in k, C * ‖g y‖) < ‖f x‖ :=
       hf.eventually (eventually_gt_atTop _)
     exact ⟨c, hc, (this.and hsl).exists.imp fun d hd => ⟨hd.2, hd.1⟩⟩
   specialize hsub c hc d hd; specialize hfd c hc d hd
-  replace hg : ∀ x ∈ Ι c d, ‖deriv f x‖ ≤ C * ‖g x‖;
-  exact fun z hz => hg c hc d hd z ⟨hz.1.le, hz.2⟩
+  replace hg : ∀ x ∈ Ι c d, ‖deriv f x‖ ≤ C * ‖g x‖ :=
+    fun z hz => hg c hc d hd z ⟨hz.1.le, hz.2⟩
   have hg_ae : ∀ᵐ x ∂volume.restrict (Ι c d), ‖deriv f x‖ ≤ C * ‖g x‖ :=
     (ae_restrict_mem measurableSet_uIoc).mono hg
-  have hsub' : Ι c d ⊆ Ι a b := uIoc_subset_uIoc_of_uIcc_subset_uIcc hsub
-  have hfi : IntervalIntegrable (deriv f) volume c d :=
-    (hgi.mono_set hsub).mono_fun' (aestronglyMeasurable_deriv _ _) hg_ae
+  have hsub' : Ι c d ⊆ k := Subset.trans Ioc_subset_Icc_self hsub
+  have hfi : IntervalIntegrable (deriv f) volume c d := by
+    rw [intervalIntegrable_iff]
+    have : IntegrableOn (fun x ↦ C * ‖g x‖) (Ι c d) := IntegrableOn.mono hgi hsub' le_rfl
+    exact Integrable.mono' this (aestronglyMeasurable_deriv _ _) hg_ae
   refine' hlt.not_le (sub_le_iff_le_add'.1 _)
   calc
     ‖f d‖ - ‖f c‖ ≤ ‖f d - f c‖ := norm_sub_norm_le _ _
-    _ = ‖∫ x in c..d, deriv f x‖ := (congr_arg _ (integral_deriv_eq_sub hfd hfi).symm)
-    _ = ‖∫ x in Ι c d, deriv f x‖ := (norm_integral_eq_norm_integral_Ioc _)
-    _ ≤ ∫ x in Ι c d, ‖deriv f x‖ := (norm_integral_le_integral_norm _)
+    _ = ‖∫ x in c..d, deriv f x‖ := congr_arg _ (integral_deriv_eq_sub hfd hfi).symm
+    _ = ‖∫ x in Ι c d, deriv f x‖ := norm_integral_eq_norm_integral_Ioc _
+    _ ≤ ∫ x in Ι c d, ‖deriv f x‖ := norm_integral_le_integral_norm _
     _ ≤ ∫ x in Ι c d, C * ‖g x‖ :=
-      (set_integral_mono_on hfi.norm.def (hgi.def.mono_set hsub') measurableSet_uIoc hg)
-    _ ≤ ∫ x in Ι a b, C * ‖g x‖ :=
-      set_integral_mono_set hgi.def (ae_of_all _ fun x => mul_nonneg hC₀ (norm_nonneg _))
-        hsub'.eventuallyLE
+      set_integral_mono_on hfi.norm.def (hgi.mono_set hsub') measurableSet_uIoc hg
+    _ ≤ ∫ x in k, C * ‖g x‖ := by
+      apply set_integral_mono_set hgi
+        (ae_of_all _ fun x => mul_nonneg hC₀ (norm_nonneg _)) hsub'.eventuallyLE
+
+theorem not_integrableOn_of_tendsto_norm_atTop_of_deriv_isBigO_filter
+    {f : ℝ → E} {g : ℝ → F}
+    {k : Set ℝ} (l : Filter ℝ) [NeBot l] [TendstoIxxClass Icc l l]
+    (hl : k ∈ l) (hd : ∀ᶠ x in l, DifferentiableAt ℝ f x) (hf : Tendsto (fun x => ‖f x‖) l atTop)
+    (hfg : deriv f =O[l] g) : ¬IntegrableOn g k := by
+  let a : E →ₗᵢ[ℝ] UniformSpace.Completion E := UniformSpace.Completion.toComplₗᵢ
+  let f' := a ∘ f
+  have h'd : ∀ᶠ x in l, DifferentiableAt ℝ f' x := by
+    filter_upwards [hd] with x hx using a.toContinuousLinearMap.differentiableAt.comp x hx
+  have h'f : Tendsto (fun x => ‖f' x‖) l atTop := hf.congr (fun x ↦ by simp)
+  have h'fg : deriv f' =O[l] g := by
+    apply IsBigO.trans _ hfg
+    rw [← isBigO_norm_norm]
+    suffices (fun x ↦ ‖deriv f' x‖) =ᶠ[l] (fun x ↦ ‖deriv f x‖) by exact this.isBigO
+    filter_upwards [hd] with x hx
+    have : deriv f' x = a (deriv f x) := by
+      rw [fderiv.comp_deriv x _ hx]
+      · have : fderiv ℝ a (f x) = a.toContinuousLinearMap := a.toContinuousLinearMap.fderiv
+        simp only [this]
+        rfl
+      · exact a.toContinuousLinearMap.differentiableAt
+    simp only [this]
+    simp
+  exact not_integrableOn_of_tendsto_norm_atTop_of_deriv_isBigO_filter_aux l hl h'd h'f h'fg
+
+/-- If `f` is eventually differentiable along a nontrivial filter `l : Filter ℝ` that is generated
+by convex sets, the norm of `f` tends to infinity along `l`, and `f' = O(g)` along `l`, where `f'`
+is the derivative of `f`, then `g` is not integrable on any interval `a..b` such that
+`[a, b] ∈ l`. -/
+theorem not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter {f : ℝ → E} {g : ℝ → F}
+    {a b : ℝ} (l : Filter ℝ) [NeBot l] [TendstoIxxClass Icc l l] (hl : [[a, b]] ∈ l)
+    (hd : ∀ᶠ x in l, DifferentiableAt ℝ f x) (hf : Tendsto (fun x => ‖f x‖) l atTop)
+    (hfg : deriv f =O[l] g) : ¬IntervalIntegrable g volume a b := by
+  rw [intervalIntegrable_iff']
+  exact not_integrableOn_of_tendsto_norm_atTop_of_deriv_isBigO_filter _ hl hd hf hfg
 set_option linter.uppercaseLean3 false in
 #align not_interval_integrable_of_tendsto_norm_at_top_of_deriv_is_O_filter not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter
 
@@ -174,3 +211,19 @@ theorem intervalIntegrable_inv_iff {a b : ℝ} :
     IntervalIntegrable (fun x => x⁻¹) volume a b ↔ a = b ∨ (0 : ℝ) ∉ [[a, b]] := by
   simp only [← intervalIntegrable_sub_inv_iff, sub_zero]
 #align interval_integrable_inv_iff intervalIntegrable_inv_iff
+
+/-- The function `fun x ↦ x⁻¹` is not integrable on any interval `[a, +∞)`. -/
+theorem not_IntegrableOn_Ici_inv {a : ℝ} :
+    ¬ IntegrableOn (fun x => x⁻¹) (Ici a) := by
+  have A : ∀ᶠ x in atTop, HasDerivAt (fun x => Real.log x) x⁻¹ x := by
+    filter_upwards [Ioi_mem_atTop 0] with x hx using Real.hasDerivAt_log (ne_of_gt hx)
+  have B : Tendsto (fun x => ‖Real.log x‖) atTop atTop :=
+    tendsto_norm_atTop_atTop.comp Real.tendsto_log_atTop
+  exact not_integrableOn_of_tendsto_norm_atTop_of_deriv_isBigO_filter atTop (Ici_mem_atTop a)
+    (A.mono (fun x hx ↦ hx.differentiableAt)) B
+    (Filter.EventuallyEq.isBigO (A.mono (fun x hx ↦ hx.deriv)))
+
+/-- The function `fun x ↦ x⁻¹` is not integrable on any interval `(a, +∞)`. -/
+theorem not_IntegrableOn_Ioi_inv {a : ℝ} :
+    ¬ IntegrableOn (·⁻¹) (Ioi a) := by
+  simpa only [IntegrableOn, restrict_Ioi_eq_restrict_Ici] using not_IntegrableOn_Ici_inv

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

This has nice performance benefits.

@@ -43,7 +43,7 @@ open scoped MeasureTheory Topology Interval NNReal ENNReal
 
 open MeasureTheory TopologicalSpace Set Filter Asymptotics intervalIntegral
 
-variable {E F : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E] [SecondCountableTopology E]
+variable {E F : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] [SecondCountableTopology E]
   [CompleteSpace E] [NormedAddCommGroup F]
 
 /-- If `f` is eventually differentiable along a nontrivial filter `l : Filter ℝ` that is generated

• 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 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.special_functions.non_integrable
-! leanprover-community/mathlib commit 55ec6e9af7d3e0043f57e394cb06a72f6275273e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.SpecialFunctions.Log.Deriv
 import Mathlib.MeasureTheory.Integral.FundThmCalculus
 
+#align_import analysis.special_functions.non_integrable from "leanprover-community/mathlib"@"55ec6e9af7d3e0043f57e394cb06a72f6275273e"
+
 /-!
 # Non integrable functions