Theorems · Theorem · number theory

NumberField.mixedEmbedding.iUnion_negAt_plusPart_ae

∀ {K : Type u_1} [inst : Field K] (A : Set (NumberField.mixedEmbedding.mixedSpace K)),
  (∀ (x : NumberField.mixedEmbedding.mixedSpace K), x ∈ A ↔ (fun w => ‖x.1 w‖, x.2) ∈ A) →
    ∀ [inst_1 : NumberField K],
      ⋃ s, ⇑(NumberField.mixedEmbedding.negAt s) '' NumberField.mixedEmbedding.plusPart A =ᵐ[MeasureTheory.volume] A

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 245 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites29

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
Setstatement and proof · cited by 53,352
Realstatement · cited by 25,697
RingHom.idstatement · cited by 18,349
MeasureTheory.Measurestatement · cited by 10,939
Fieldstatement and proof · cited by 7,404
Set.imagestatement and proof · cited by 5,609
Complexstatement · cited by 5,565
Norm.normstatement and proof · cited by 5,413
Set.iUnionstatement and proof · cited by 2,483
MeasureTheory.aestatement and proof · cited by 2,352
Filter.EventuallyEqstatement and proof · cited by 1,912

Cited by1

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.volume_eq_two_pow_mul_volume_plusPartproof · cited by 1