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fix: label Example 11.5.5 / Cor. 11.5.2 sharpness; tidy Lusin docstring #625

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fix: label Example 11.5.5 / Cor. 11.5.2 sharpness; tidy Lusin docstring #625

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8c72237
fix: drop stray space in Exercise 1.3.23 Lusin docstring
Chessing234 Aug 4, 2026
35c7409
fix: part-label Example 11.5.5 Verso docs (a)–(e)
Chessing234 Aug 4, 2026
c2f07fe
fix: label 1/x examples as Cor. 11.5.2 sharpness
Chessing234 Aug 4, 2026
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2 changes: 1 addition & 1 deletion Analysis/MeasureTheory/Section_1_3_5.lean
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Expand Up @@ -1568,7 +1568,7 @@ example : ∃ (d:ℕ) (f : EuclideanSpace' d → ℝ),
def LocallyComplexAbsolutelyIntegrable {d:ℕ} (f: EuclideanSpace' d → ℂ) : Prop :=
∀ (S: Set (EuclideanSpace' d)), LebesgueMeasurable S ∧ Bornology.IsBounded S → ComplexAbsolutelyIntegrableOn f S

/-- Exercise 1.3.23 (Lusin's theorem only requires local absolute integrability ). -/
/-- Exercise 1.3.23 (Lusin's theorem only requires local absolute integrability). -/
theorem LocallyComplexAbsolutelyIntegrable.approx_by_continuous_outside_small {d:ℕ} {f : EuclideanSpace' d → ℂ}
(hf: LocallyComplexAbsolutelyIntegrable f)
(ε : ℝ) (hε : 0 < ε) :
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7 changes: 7 additions & 0 deletions Analysis/Section_11_5.lean
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Expand Up @@ -83,8 +83,10 @@ theorem integ_of_uniform_cts {I: BoundedInterval} {f:ℝ → ℝ} (hf: UniformCo
theorem integ_of_cts {a b:ℝ} {f:ℝ → ℝ} (hf: ContinuousOn f (Icc a b)) :
IntegrableOn f (Icc a b) := integ_of_uniform_cts (UniformContinuousOn.of_continuousOn hf)

/-- Corollary 11.5.2 (sharpness) (a) -/
example : ¬ ContinuousOn (fun x:ℝ ↦ 1/x) (Icc 0 1) := by sorry

/-- Corollary 11.5.2 (sharpness) (b) -/
example : ¬ IntegrableOn (fun x:ℝ ↦ 1/x) (Icc 0 1) := by sorry

open PiecewiseConstantOn ConstantOn in
Expand Down Expand Up @@ -203,14 +205,19 @@ noncomputable abbrev f_11_5_5 : ℝ → ℝ := fun x ↦
else if x = 2 then 7
else x^3

/-- Example 11.5.5 (a) -/
example : ¬ ContinuousOn f_11_5_5 (Icc 1 3) := by sorry

/-- Example 11.5.5 (b) -/
example : ContinuousOn f_11_5_5 (Ico 1 2) := by sorry

/-- Example 11.5.5 (c) -/
example : ContinuousOn f_11_5_5 (Icc 2 2) := by sorry

/-- Example 11.5.5 (d) -/
example : ContinuousOn f_11_5_5 (Ioc 2 3) := by sorry

/-- Example 11.5.5 (e) -/
example : PiecewiseContinuousOn f_11_5_5 (Icc 1 3) := by sorry

/-- Proposition 11.5.6 / Exercise 11.5.1 -/
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