Theorems · Theorem · complex analysis
MeromorphicOn.intervalIntegrable_posLog_norm_meromorphicOn
Deprecated since 2026-03-28Use MeromorphicOn.intervalIntegrable_posLog_norm instead.
∀ {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 bAlias of MeromorphicOn.intervalIntegrable_posLog_norm.
If f is real-meromorphic on a compact interval, then log ‖f ·‖ is interval integrable on this
interval.
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- 0 results in Mathlib
- Foundations
- Depth 271 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- NormedAddCommGroupstatement · cited by 15,752
- NormedSpacestatement · cited by 12,499
- Norm.normstatement · cited by 5,413
- MeasureTheory.MeasureSpace.volumestatement · cited by 1,323
- Set.uIccstatement · cited by 393
- IntervalIntegrablestatement · cited by 316
- MeromorphicOnstatement · cited by 141
- Real.posLogstatement · cited by 61
- MeromorphicOn.intervalIntegrable_posLog_normproof · cited by 1
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