Theorems · Theorem · complex analysis
ValueDistribution.proximity_top
∀ {E : Type u_1} [inst : NormedAddCommGroup E] {f : ℂ → E},
ValueDistribution.proximity f ⊤ = Real.circleAverage (fun x => ‖f x‖.posLog) 0Expand the definition of proximity f a in case where a₀ = ⊤.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 253 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Top.topstatement and proof · cited by 9,680
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- WithTopstatement · cited by 3,754
- Real.circleAveragestatement and proof · cited by 106
- Real.posLogstatement and proof · cited by 61
- ValueDistribution.proximitystatement · cited by 28
Cited by3
Results whose statement or proof uses this declaration.
- ValueDistribution.characteristic_top_eq_circleAverage_add_circleAverageproof · cited by 3
- ValueDistribution.proximity_invproof · cited by 2
- ValueDistribution.proximity_sum_top_leproof · cited by 2