Skip to content

fix: ContinuousOn 1/x on [0,1] is false; split Ex. 11.3.1 labels #613

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
teorth merged 1 commit into from
Aug 2, 2026
+3 −3
Merged

fix: ContinuousOn 1/x on [0,1] is false; split Ex. 11.3.1 labels #613

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
4 changes: 2 additions & 2 deletions Analysis/Section_11_3.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -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
Expand Down
2 changes: 1 addition & 1 deletion Analysis/Section_11_5.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -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

Expand Down
Loading