circleAverage_log_norm_sub_const_eq_log_radius_add_posLog

∀ {a c : ℂ} {R : ℝ}, R ≠ 0 → Real.circleAverage (fun x => Real.log ‖x - a‖) c R = Real.log R + (R⁻¹ * ‖c - a‖).posLog

Generalization of circleAverage_log_norm_sub_const_eq_posLog: The circleAverage (log ‖· - a‖) c R equals log R + log⁺ (|R|⁻¹ * ‖c - a‖).

Defined in: Mathlib.Analysis.SpecialFunctions.Integrals.PosLogEqCircleAverage
Cited by: 1 results in Mathlib
Foundations: Depth 294 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Results whose statement or proof uses this declaration.