Theorems · Theorem · number theory

NumberField.Set.HasDirichletDensity.nonneg

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K]
  {S : Set (IsDedekindDomain.HeightOneSpectrum (NumberField.RingOfIntegers K))} {δ : ℝ},
  NumberField.Set.HasDirichletDensity S δ → 0 ≤ δ

The Dirichlet density is nonnegative.

Defined in: Mathlib.NumberTheory.NumberField.DirichletDensity
Cited by: 1 results in Mathlib
Foundations: Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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

Setstatement and proof · cited by 53,352
Realstatement and proof · cited by 25,697
Fieldstatement and proof · cited by 7,404
Set.univproof · cited by 3,945
NumberFieldstatement and proof · cited by 653
Filter.Eventually.of_forallproof · cited by 526
NumberField.RingOfIntegersstatement and proof · cited by 413
IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
div_nonnegproof · cited by 103
ge_of_tendstoproof · cited by 29
NumberField.Set.HasDirichletDensitystatement and proof · cited by 8
NumberField.Set.primeIdealZetaSum_nonnegproof · cited by 1

Cited by1

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NumberField.Set.dirichletDensity_nonnegproof · cited by 0