Theorems · Theorem · measure theory
EuclideanSpace.volume_preserving_symm_measurableEquiv_toLp
∀ (ι : Type u_4) [inst : Fintype ι], MeasureTheory.MeasurePreserving (⇑(MeasurableEquiv.toLp 2 (ι → ℝ)).symm) MeasureTheory.volume MeasureTheory.volume
The measure equivalence between EuclideanSpace ℝ ι and ι → ℝ is volume preserving.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 265 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.
Cites31
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
- Realstatement and proof · cited by 25,697
- MeasurableSpaceproof · cited by 13,106
- MeasureTheory.Measureproof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Fintypestatement and proof · cited by 7,736
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- MeasureTheory.Measure.mapproof · cited by 858
- ContinuousLinearEquiv.symmproof · cited by 368
- WithLpstatement and proof · cited by 345
- MeasurableEquivstatement · cited by 269
- MeasureTheory.MeasurePreservingstatement and proof · cited by 259
Cited by4
Results whose statement or proof uses this declaration.
- PiLp.volume_preserving_toLpproof · cited by 5
- WithLp.volume_preserving_symm_measurableEquiv_toLp_prodproof · cited by 2
- PiLp.volume_preserving_ofLpproof · cited by 0
- ZLattice.covolume_div_covolume_eq_relIndex'proof · cited by 0