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Theorems · Theorem · complex analysis

ValueDistribution.logCounting_const_zero

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] [inst_1 : ProperSpace 𝕜] {E : Type u_2}
  [inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace 𝕜 E] {e : WithTop E}, ValueDistribution.logCounting 0 e = 0

The logarithmic counting function of the constant function zero is zero.

Defined in
Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic
Cited by
1 results in Mathlib
Foundations
Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldProperSpaceNormedAddCommGroupNormedSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ValueDistribution.logCounting_sum_top_le · cited by 2ValueDistribution.logCoun…Real · cited by 25697RealNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldWithTop · cited by 3754WithTopProperSpace · cited by 190ProperSpaceValueDistribution.logCounting · cited by 45ValueDistribution.logCoun…ValueDistribution.logCounting_const · cited by 1ValueDistribution.logCoun…ValueDistribution.logCounting…CITED BYCITES

Cites8

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Cited by1

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