Theorems · Theorem · complex analysis

ValueDistribution.logCounting_nonneg

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] [inst_1 : ProperSpace 𝕜] {E : Type u_2}
  [inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace 𝕜 E] {r : ℝ} {f : 𝕜 → E} {e : WithTop E},
  1 ≤ r → 0 ≤ ValueDistribution.logCounting f e r

For 1 ≤ r, the logarithmic counting function is non-negative.

Defined in

Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic

Cited by

2 results in Mathlib

Foundations

Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldProperSpaceNormedAddCommGroupNormedSpace