Theorems · Theorem · real analysis
intervalIntegral.intervalIntegrable_one_div
∀ {a b : ℝ} {f : ℝ → ℝ} {μ : MeasureTheory.Measure ℝ} [MeasureTheory.IsLocallyFiniteMeasure μ],
(∀ x ∈ Set.uIcc a b, f x ≠ 0) → ContinuousOn f (Set.uIcc a b) → IntervalIntegrable (fun x => 1 / f x) μ a b- Cited by
- 2 results in Mathlib
- Foundations
- Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ContinuousOnstatement and proof · cited by 1,411
- Set.uIccstatement and proof · cited by 393
- IntervalIntegrablestatement · cited by 316
- MeasureTheory.IsLocallyFiniteMeasurestatement and proof · cited by 171
- continuousOn_constproof · cited by 96
- ContinuousOn.intervalIntegrableproof · cited by 27
- ContinuousOn.divproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- ZetaAsymptotics.term_oneproof · cited by 1
- intervalIntegral.intervalIntegrable_invproof · cited by 0