diff --git a/Analysis/Section_11_3.lean b/Analysis/Section_11_3.lean index cb0b8763..a69eae7a 100644 --- a/Analysis/Section_11_3.lean +++ b/Analysis/Section_11_3.lean @@ -177,12 +177,12 @@ theorem lower_integ_eq_sup_lower_sum {f:ℝ → ℝ} {I:BoundedInterval} (hf: Bd lower_integral f I = sSup (.range (fun P : Partition I ↦ lower_riemann_sum f P)) := by sorry -/-- Exercise 11.3.1 -/ +/-- Exercise 11.3.1 (i) -/ theorem MajorizesOn.trans {f g h: ℝ → ℝ} {I: BoundedInterval} (hfg: MajorizesOn f g I) (hgh: MajorizesOn g h I) : MajorizesOn f h I := by sorry -/-- Exercise 11.3.1 -/ +/-- Exercise 11.3.1 (ii) -/ theorem MajorizesOn.anti_symm {f g: ℝ → ℝ} {I: BoundedInterval}: (∀ x ∈ (I:Set ℝ), f x = g x) ↔ MajorizesOn f g I ∧ MajorizesOn g f I := by sorry diff --git a/Analysis/Section_11_5.lean b/Analysis/Section_11_5.lean index 29fa5279..d23b322e 100644 --- a/Analysis/Section_11_5.lean +++ b/Analysis/Section_11_5.lean @@ -83,7 +83,7 @@ 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) -example : ContinuousOn (fun x:ℝ ↦ 1/x) (Icc 0 1) := by sorry +example : ¬ ContinuousOn (fun x:ℝ ↦ 1/x) (Icc 0 1) := by sorry example : ¬ IntegrableOn (fun x:ℝ ↦ 1/x) (Icc 0 1) := by sorry