Theorems · Theorem · number theory

NumberField.mixedEmbedding.lintegral_comp_polarSpaceCoord_symm

∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K] (f : NumberField.mixedEmbedding.mixedSpace K → ENNReal),
  ∫⁻ (x : NumberField.mixedEmbedding.polarSpace K) in (NumberField.mixedEmbedding.polarSpaceCoord K).target,
      (∏ w, ENNReal.ofReal (x.1 ↑w)) * f (↑(NumberField.mixedEmbedding.polarSpaceCoord K).symm x) =
    ∫⁻ (x : NumberField.mixedEmbedding.mixedSpace K), f x

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord
Cited by: 1 results in Mathlib
Foundations: Depth 280 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites46

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

DFunLike.coeproof · cited by 62,936
Setproof · cited by 53,352
Realstatement and proof · cited by 25,697
ENNRealstatement and proof · cited by 9,879
Fieldstatement and proof · cited by 7,404
Complexstatement · cited by 5,565
Set.preimageproof · cited by 4,946
Set.univproof · cited by 3,945
Finset.univstatement and proof · cited by 3,473
Finset.prodstatement and proof · cited by 2,356
SProd.sprodproof · cited by 1,750
MeasureTheory.Measure.restrictstatement and proof · cited by 1,646

Cited by1

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.volume_eq_two_pi_pow_mul_integralproof · cited by 1