Theorems · Theorem · complex analysis
MeromorphicOn.intervalIntegrable_posLog_norm
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : ℝ → E} {a b : ℝ},
MeromorphicOn f (Set.uIcc a b) → IntervalIntegrable (fun x => ‖f x‖.posLog) MeasureTheory.volume a bIf f is real-meromorphic on a compact interval, then log ‖f ·‖ is interval integrable on this
interval.
- Cited by
- 1 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.
Cites16
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Norm.normstatement and proof · cited by 5,413
- absproof · cited by 1,814
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- Real.logproof · cited by 939
- mul_addproof · cited by 413
- Set.uIccstatement and proof · cited by 393
- IntervalIntegrablestatement and proof · cited by 316
- MeromorphicOnstatement and proof · cited by 141
- Real.posLogstatement · cited by 61
Cited by1
Results whose statement or proof uses this declaration.
- MeromorphicOn.intervalIntegrable_posLog_norm_meromorphicOnproof · cited by 0