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fix: label Ex. 1.2.2' and Ex. 9.2.1 (a)–(d) #614

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teorth merged 2 commits into from
Aug 3, 2026
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fix: label Ex. 1.2.2' and Ex. 9.2.1 (a)–(d) #614

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08406b8
fix: label Ex. 1.2.2 (i)/(ii) and Ex. 9.2.1 (a)–(d)
Chessing234 Aug 3, 2026
615ac74
fix: label Ex. 1.2.2' instead of inventing (i)/(ii)
Chessing234 Aug 3, 2026
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2 changes: 1 addition & 1 deletion Analysis/MeasureTheory/Section_1_2_0.lean
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Expand Up @@ -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' -/
-- 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.
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6 changes: 4 additions & 2 deletions Analysis/Section_9_2.lean
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Expand Up @@ -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
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