Theorems · Theorem · complex analysis
MeromorphicOn.circleIntegrable_log_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 => Real.log ‖f x‖) c RIf f is complex meromorphic on a circle in the complex plane, then log ‖f ·‖ is circle
integrable over that circle.
- Cited by
- 11 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.
Cites60
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Top.topproof · cited by 9,680
- Set.Elemproof · cited by 7,166
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- Filter.EventuallyEqproof · cited by 1,912
- absstatement and proof · cited by 1,814
- Real.piproof · cited by 1,774
- Filter.univ_mem'proof · cited by 1,672
Cited by11
Results whose statement or proof uses this declaration.
- MeromorphicOn.circleIntegrable_posLog_normproof · cited by 7
- MeromorphicOn.circleAverage_log_normproof · cited by 3
- Polynomial.intervalIntegrable_mahlerMeasureproof · cited by 2
- circleIntegrable_log_norm_sub_constproof · cited by 2
- circleAverage_log_norm_factorizedRationalproof · cited by 1
- circleAverage_log_norm_sub_const_eq_log_radius_add_posLogproof · cited by 1
- MeromorphicOn.circleIntegrable_log_norm_of_nonnegproof · cited by 1
- circleIntegrable_log_norm_factorizedRationalproof · cited by 1
- Polynomial.mahlerMeasure_le_sqrt_sum_sq_norm_coeffproof · cited by 1
- circleIntegrable_log_norm_meromorphicOnproof · cited by 0
- AnalyticOnNhd.sum_divisor_leproof · cited by 0