Theorems · Theorem · complex analysis
MeromorphicOn.circleIntegrable_posLog_norm
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {c : ℂ} {R : ℝ} {f : ℂ → E},
MeromorphicOn f (Metric.sphere c |R|) → CircleIntegrable (fun x => ‖f x‖.posLog) c RIf f is complex meromorphic on a circle in the complex plane, then log⁺ ‖f ·‖ is circle
integrable over that circle.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 271 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
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- absstatement and proof · cited by 1,814
- Real.logproof · cited by 939
- mul_addproof · cited by 413
- Metric.spherestatement and proof · cited by 371
- MeromorphicOnstatement and proof · cited by 141
- CircleIntegrablestatement and proof · cited by 86
- Real.posLogstatement · cited by 61
Cited by7
Results whose statement or proof uses this declaration.
- ValueDistribution.proximity_mul_top_leproof · cited by 2
- ValueDistribution.proximity_sum_top_leproof · cited by 2
- MeromorphicOn.circleIntegrable_posLog_norm_of_nonnegproof · cited by 1
- ValueDistribution.proximity_sub_proximity_inv_eq_circleAverageproof · cited by 1
- ValueDistribution.abs_characteristic_sub_characteristic_shift_leproof · cited by 1
- ValueDistribution.Cartan.integrable_integral_norm_cartanKernelproof · cited by 1
- circleIntegrable_posLog_norm_meromorphicOnproof · cited by 0