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Theorems · Theorem · number theory

NumberField.Set.dirichletDensity_nonneg

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

The Dirichlet density of S is nonnegative.

Defined in
Mathlib.NumberTheory.NumberField.DirichletDensity
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Foundations
Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldNumberField
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Set · cited by 53352SetReal · cited by 25697RealField · cited by 7404Fieldle_rfl · cited by 1558le_rflNumberField · cited by 653NumberFieldNumberField.RingOfIntegers · cited by 413NumberField.RingOfIntegersIsDedekindDomain.HeightOneSpectrum · cited by 338IsDedekindDomain.HeightOn…NumberField.Set.HasDirichletDensity · cited by 8Set.HasDirichletDensityNumberField.Set.dirichletDensity · cited by 5Set.dirichletDensityNumberField.Set.HasDirichletDensity.nonneg · cited by 1HasDirichletDensity.nonnegSet.dirichletDensity_nonnegCITED BYCITES

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