Theorems · Theorem · measure theory
OrthonormalBasis.addHaar_eq_volume
∀ {ι : Type u_4} {F : Type u_5} [inst : Fintype ι] [inst_1 : NormedAddCommGroup F] [inst_2 : InnerProductSpace ℝ F]
[inst_3 : FiniteDimensional ℝ F] [inst_4 : MeasurableSpace F] [inst_5 : BorelSpace F] (b : OrthonormalBasis ι ℝ F),
b.toBasis.addHaar = MeasureTheory.volumeThe Haar measure defined by any orthonormal basis of a finite-dimensional inner product space is equal to its volume measure.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 264 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
- Fintypestatement and proof · cited by 7,736
- InnerProductSpacestatement and proof · cited by 3,523
- FiniteDimensionalstatement and proof · cited by 1,854
- BorelSpacestatement and proof · cited by 1,602
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- OrthonormalBasisstatement and proof · cited by 188
- OrthonormalBasis.toBasisstatement and proof · cited by 102
- Module.Basis.addHaarstatement · cited by 15
Cited by4
Results whose statement or proof uses this declaration.
- LinearIsometryEquiv.measurePreservingproof · cited by 8
- EuclideanSpace.volume_preserving_symm_measurableEquiv_toLpproof · cited by 4
- OrthonormalBasis.measurePreserving_measurableEquivproof · cited by 2
- NumberField.mixedEmbedding.euclidean.volumePreserving_toMixedproof · cited by 2