Theorems · Theorem · complex analysis

ValueDistribution.logCounting_add_const

∀ {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} {a₀ : E},
  Meromorphic f → ValueDistribution.logCounting (f + fun x => a₀) ⊤ = ValueDistribution.logCounting f ⊤

Special case of logCounting_add_analyticOn: Adding a constant does not change the logarithmic counting function for the poles.

Defined in

Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic

Cited by

1 results in Mathlib

Foundations

Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldProperSpaceNormedAddCommGroupNormedSpace