Theorems · Theorem · real analysis
IntervalIntegrable.log
∀ {a b : ℝ} {f : ℝ → ℝ} {μ : MeasureTheory.Measure ℝ} [MeasureTheory.IsLocallyFiniteMeasure μ],
ContinuousOn f (Set.uIcc a b) → (∀ x ∈ Set.uIcc a b, f x ≠ 0) → IntervalIntegrable (fun x => Real.log (f x)) μ a b- Cited by
- 1 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
- Real.logstatement · cited by 939
- Set.uIccstatement and proof · cited by 393
- IntervalIntegrablestatement · cited by 316
- MeasureTheory.IsLocallyFiniteMeasurestatement and proof · cited by 171
- ContinuousOn.intervalIntegrableproof · cited by 27
- ContinuousOn.logproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- intervalIntegral.intervalIntegrable_logproof · cited by 0