Theorems · Theorem · complex analysis

MeromorphicOn.intervalIntegrable_log_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 => Real.log ‖f x‖) MeasureTheory.volume a b

If f is real-meromorphic on a compact interval, then log ‖f ·‖ is interval integrable on this interval.

Defined in

Mathlib.Analysis.SpecialFunctions.Integrability.LogMeromorphic

Cited by

4 results in Mathlib

Foundations

Depth 269 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace