Theorems · Theorem · measure theory
MeasureTheory.addHaarMeasure_eq_volume_pi
∀ (ι : Type u_1) [inst : Fintype ι], MeasureTheory.Measure.addHaarMeasure (TopologicalSpace.PositiveCompacts.piIcc01 ι) = MeasureTheory.volume
The Haar measure equals the Lebesgue measure on ℝ^ι.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 246 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealproof · cited by 9,879
- SetLike.coeproof · cited by 8,199
- Fintypestatement and proof · cited by 7,736
- Set.univproof · cited by 3,945
- Finset.univproof · cited by 3,473
- Set.Iccproof · cited by 1,702
- one_smulproof · cited by 1,374
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- sub_zeroproof · cited by 938
Cited by3
Results whose statement or proof uses this declaration.
- EuclideanSpace.volume_preserving_symm_measurableEquiv_toLpproof · cited by 4
- Complex.volume_preserving_equiv_piproof · cited by 2
- MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaarproof · cited by 1