Theorems · Theorem · complex analysis

ValueDistribution.logCounting_monotoneOn

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] [inst_1 : ProperSpace 𝕜] {E : Type u_2}
  [inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace 𝕜 E] {f : 𝕜 → E} {e : WithTop E},
  MonotoneOn (ValueDistribution.logCounting f e) (Set.Ioi 0)

The logarithmic counting function is monotonous.

Defined in: Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NontriviallyNormedField ProperSpace NormedAddCommGroup NormedSpace

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Cites16

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
NormedSpacestatement and proof · cited by 12,499
Top.topproof · cited by 9,680
NontriviallyNormedFieldstatement and proof · cited by 8,742
Set.univproof · cited by 3,945
WithTopstatement and proof · cited by 3,754
Set.Ioistatement and proof · cited by 1,463
MonotoneOnstatement and proof · cited by 311
ProperSpacestatement and proof · cited by 190
MeromorphicOn.divisorproof · cited by 90
WithTop.untop₀proof · cited by 73

Cited by1

Results whose statement or proof uses this declaration.

ValueDistribution.characteristic_monotoneOnproof · cited by 0