From 08406b8ce138b4f1f1fd920d09137b9bcfbd3e5b Mon Sep 17 00:00:00 2001 From: Taksh Date: Mon, 3 Aug 2026 14:44:19 +0530 Subject: [PATCH 1/2] =?UTF-8?q?fix:=20label=20Ex.=201.2.2=20(i)/(ii)=20and?= =?UTF-8?q?=20Ex.=209.2.1=20(a)=E2=80=93(d)?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Drop the 1.2.22 hunk — already disambiguated on main. Keep the missing 9.2.1 (c)/(d) Verso docs Tao asked for. --- Analysis/MeasureTheory/Section_1_2_0.lean | 4 ++-- Analysis/Section_9_2.lean | 6 ++++-- 2 files changed, 6 insertions(+), 4 deletions(-) diff --git a/Analysis/MeasureTheory/Section_1_2_0.lean b/Analysis/MeasureTheory/Section_1_2_0.lean index f61b9aae4..4806a8bab 100644 --- a/Analysis/MeasureTheory/Section_1_2_0.lean +++ b/Analysis/MeasureTheory/Section_1_2_0.lean @@ -573,7 +573,7 @@ example : -/-- Exercise 1.2.2 -/ +/-- Exercise 1.2.2 (i) -/ -- The pointwise limit of uniformly bounded Riemann integrable functions need not be Riemann integrable. example : ∃ f: ℕ → ℝ → ℝ, ∃ F: ℝ → ℝ, ∃ M, ∀ n, ∀ x ∈ Set.Icc 0 1, |f n x| ≤ M ∧ (∀ x ∈ Set.Icc 0 1, Filter.atTop.Tendsto (fun n ↦ f n x) (nhds (F x))) ∧ @@ -581,7 +581,7 @@ example : ∃ f: ℕ → ℝ → ℝ, ∃ F: ℝ → ℝ, ∃ M, ∀ n, ∀ x ¬ RiemannIntegrableOn F (Icc 0 1) := by sorry -/-- Exercise 1.2.2 -/ +/-- Exercise 1.2.2 (ii) -/ -- Determine whether uniform convergence of uniformly bounded Riemann integrable functions preserves Riemann integrability (true or false). def Ex_1_2_2b : Decidable ( ∀ f: ℕ → ℝ → ℝ, ∀ F: ℝ → ℝ, (∃ M, ∀ n, ∀ x ∈ Set.Icc 0 1, |f n x| ≤ M) → (∀ x ∈ Set.Icc 0 1, TendstoUniformly f F Filter.atTop) → (∀ n, RiemannIntegrableOn (f n) (Icc 0 1)) → RiemannIntegrableOn F (Icc 0 1) ) := by -- the first line of this construction should be either `apply isTrue` or `apply isFalse`, depending on whether you believe the given statement to be true or false. diff --git a/Analysis/Section_9_2.lean b/Analysis/Section_9_2.lean index dda4c38e4..d96d8a1db 100644 --- a/Analysis/Section_9_2.lean +++ b/Analysis/Section_9_2.lean @@ -51,20 +51,22 @@ example : f_9_2_2 ∘ g_9_2_2 = fun x ↦ 4*x^2 := by grind example : g_9_2_2 ∘ f_9_2_2 = fun x ↦ 2*x^2 := by grind -/-- Exercise 9.2.1. -/ +/-- Exercise 9.2.1 (a) -/ def Exercise_9_2_1a : Decidable (∀ (f g h : ℝ → ℝ), (f+g) ∘ h = f ∘ h + g ∘ h) := by -- The first line of this construction should be `apply isTrue` or `apply isFalse`. sorry -/-- Exercise 9.2.1. -/ +/-- Exercise 9.2.1 (b) -/ def Exercise_9_2_1b : Decidable (∀ (f g h : ℝ → ℝ), f ∘ (g + h) = f ∘ g + f ∘ h) := by -- The first line of this construction should be `apply isTrue` or `apply isFalse`. sorry +/-- Exercise 9.2.1 (c) -/ def Exercise_9_2_1c : Decidable (∀ (f g h : ℝ → ℝ), (f+g) * h = f * h + g * h) := by -- The first line of this construction should be `apply isTrue` or `apply isFalse`. sorry +/-- Exercise 9.2.1 (d) -/ def Exercise_9_2_1d : Decidable (∀ (f g h : ℝ → ℝ), f * (g+h) = f * g + f * h) := by -- The first line of this construction should be `apply isTrue` or `apply isFalse`. sorry From 615ac74ccee4c926101d7558445ce1da093e07f8 Mon Sep 17 00:00:00 2001 From: Taksh Date: Mon, 3 Aug 2026 21:54:40 +0530 Subject: [PATCH 2/2] fix: label Ex. 1.2.2' instead of inventing (i)/(ii) Text has two questions in one exercise; follow the primed-variant convention from 7a9e513. Leave 1.2.22 to #632. --- Analysis/MeasureTheory/Section_1_2_0.lean | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/Analysis/MeasureTheory/Section_1_2_0.lean b/Analysis/MeasureTheory/Section_1_2_0.lean index 4806a8bab..93e4cfa53 100644 --- a/Analysis/MeasureTheory/Section_1_2_0.lean +++ b/Analysis/MeasureTheory/Section_1_2_0.lean @@ -573,7 +573,7 @@ example : -/-- Exercise 1.2.2 (i) -/ +/-- Exercise 1.2.2 -/ -- The pointwise limit of uniformly bounded Riemann integrable functions need not be Riemann integrable. example : ∃ f: ℕ → ℝ → ℝ, ∃ F: ℝ → ℝ, ∃ M, ∀ n, ∀ x ∈ Set.Icc 0 1, |f n x| ≤ M ∧ (∀ x ∈ Set.Icc 0 1, Filter.atTop.Tendsto (fun n ↦ f n x) (nhds (F x))) ∧ @@ -581,7 +581,7 @@ example : ∃ f: ℕ → ℝ → ℝ, ∃ F: ℝ → ℝ, ∃ M, ∀ n, ∀ x ¬ RiemannIntegrableOn F (Icc 0 1) := by sorry -/-- Exercise 1.2.2 (ii) -/ +/-- Exercise 1.2.2' -/ -- Determine whether uniform convergence of uniformly bounded Riemann integrable functions preserves Riemann integrability (true or false). def Ex_1_2_2b : Decidable ( ∀ f: ℕ → ℝ → ℝ, ∀ F: ℝ → ℝ, (∃ M, ∀ n, ∀ x ∈ Set.Icc 0 1, |f n x| ≤ M) → (∀ x ∈ Set.Icc 0 1, TendstoUniformly f F Filter.atTop) → (∀ n, RiemannIntegrableOn (f n) (Icc 0 1)) → RiemannIntegrableOn F (Icc 0 1) ) := by -- the first line of this construction should be either `apply isTrue` or `apply isFalse`, depending on whether you believe the given statement to be true or false.