Theorems · Theorem · number theory

NumberField.mixedEmbedding.volume_negAt_plusPart

∀ {K : Type u_1} [inst : Field K] {s : Set { w // w.IsReal }} {A : Set (NumberField.mixedEmbedding.mixedSpace K)}
  [inst_1 : NumberField K],
  MeasurableSet A →
    MeasureTheory.volume (⇑(NumberField.mixedEmbedding.negAt s) '' NumberField.mixedEmbedding.plusPart A) =
      MeasureTheory.volume (NumberField.mixedEmbedding.plusPart A)

The image of the plusPart of A by negAt have all the same volume as plusPart A.

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 281 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.

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Complexstatement · cited by 5,565
MeasurableSetstatement and proof · cited by 3,075
MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
ContinuousLinearEquivstatement and proof · cited by 743

Cited by1

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NumberField.mixedEmbedding.volume_eq_two_pow_mul_volume_plusPartproof · cited by 1