Theorems · Theorem · complex analysis

Function.locallyFinsuppWithin.logCounting_nonneg

∀ {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : ProperSpace E] {f : Function.locallyFinsupp E ℤ} {r : ℝ},
  0 ≤ f → 1 ≤ r → 0 ≤ Function.locallyFinsuppWithin.logCounting f r

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

Defined in: Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic
Cited by: 3 results in Mathlib
Foundations: Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup ProperSpace

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites35

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Realstatement and proof · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
Norm.normproof · cited by 5,413
Set.univstatement · cited by 3,945
AddMonoidHomstatement · cited by 3,230
Nat.cast_oneproof · cited by 2,501
mul_commproof · cited by 2,262
MulZeroClass.mul_zeroproof · cited by 2,091
Nat.cast_zeroproof · cited by 1,870
absproof · cited by 1,814
MulZeroClass.zero_mulproof · cited by 1,625

Cited by3

Results whose statement or proof uses this declaration.

Function.locallyFinsuppWithin.logCounting_leproof · cited by 5
ValueDistribution.logCounting_nonnegproof · cited by 2
Function.locallyFinsuppWithin.zero_iff_logCounting_boundedproof · cited by 1