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Theorems · Theorem · number theory

NumberField.Set.dirichletDensity_empty

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K], NumberField.Set.dirichletDensity ∅ = 0

The Dirichlet density of the empty set is 0.

Defined in
Mathlib.NumberTheory.NumberField.DirichletDensity
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Foundations
Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldNumberField
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Set · cited by 53352SetReal · cited by 25697RealField · cited by 7404FieldNumberField · cited by 653NumberFieldNumberField.RingOfIntegers · cited by 413NumberField.RingOfIntegersIsDedekindDomain.HeightOneSpectrum · cited by 338IsDedekindDomain.HeightOn…NumberField.Set.dirichletDensity · cited by 5Set.dirichletDensityNumberField.Set.HasDirichletDensity.dirichletDensity_eq · cited by 1HasDirichletDensity.diric…NumberField.Set.hasDirichletDensity_empty · cited by 1Set.hasDirichletDensity_e…Set.dirichletDensity_emptyCITED BYCITES

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