Theorems · Theorem · real analysis
circleAverage_log_norm_sub_const_eq_posLog
∀ {a : ℂ}, Real.circleAverage (fun x => Real.log ‖x - a‖) 0 1 = ‖a‖.posLogThe circleAverage (log ‖· - a‖) 0 1 equals log⁺ ‖a‖.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 292 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- le_of_ltproof · cited by 1,175
- Real.logstatement · cited by 939
- lt_trichotomyproof · cited by 178
- Real.circleAveragestatement · cited by 106
- Real.posLogstatement and proof · cited by 61
- abs_normproof · cited by 36
- Real.posLog_eq_zero_iffproof · cited by 4
- Real.posLog_eq_logproof · cited by 3
- circleAverage_log_norm_sub_const₀proof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.logMahlerMeasure_X_sub_Cproof · cited by 2
- ValueDistribution.circleAverage_circleAverage_eq_proximity_topproof · cited by 1
- circleAverage_log_norm_add_const_eq_posLogproof · cited by 1