Theorems · Theorem · complex analysis
MeromorphicOn.intervalIntegrable_log
∀ {a b : ℝ} {f : ℝ → ℝ}, MeromorphicOn f (Set.uIcc a b) → IntervalIntegrable (Real.log ∘ f) MeasureTheory.volume a bIf f is real-meromorphic on a compact interval, then log ∘ f is interval integrable on this
interval.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 270 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- Real.logstatement and proof · cited by 939
- Set.uIccstatement and proof · cited by 393
- IntervalIntegrablestatement and proof · cited by 316
- MeromorphicOnstatement and proof · cited by 141
- Real.log_absproof · cited by 17
- MeromorphicOn.intervalIntegrable_log_normproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- intervalIntegrable_log_cosproof · cited by 1
- intervalIntegrable_log_sinproof · cited by 1