Theorems · Theorem · real analysis
circleAverage_log_norm_sub_const_of_mem_closedBall
∀ {a c : ℂ} {R : ℝ}, a ∈ Metric.closedBall c |R| → Real.circleAverage (fun x => Real.log ‖x - a‖) c R = Real.log RTrivial corollary of
circleAverage_log_norm_sub_const_eq_log_radius_add_posLog: If u : ℂ lies within the closed ball
with center c and radius R, then the circle average
circleAverage (log ‖· - u‖) c R equals log R.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 295 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- absstatement and proof · cited by 1,814
- sub_selfproof · cited by 996
- Real.logstatement and proof · cited by 939
- norm_nonnegproof · cited by 725
- Metric.closedBallstatement and proof · cited by 704
- norm_zeroproof · cited by 366
- abs_of_nonnegproof · cited by 279
- abs_nonnegproof · cited by 168
Cited by1
Results whose statement or proof uses this declaration.
- circleAverage_log_norm_factorizedRationalproof · cited by 1