Theorems · Theorem · measure theory
OrthonormalBasis.measurePreserving_measurableEquiv
∀ {ι : Type u_1} {F : Type u_3} [inst : NormedAddCommGroup F] [inst_1 : InnerProductSpace ℝ F]
[inst_2 : MeasurableSpace F] [inst_3 : BorelSpace F] [inst_4 : Fintype ι] [inst_5 : FiniteDimensional ℝ F]
(b : OrthonormalBasis ι ℝ F),
MeasureTheory.MeasurePreserving (⇑b.measurableEquiv) MeasureTheory.volume MeasureTheory.volumeThe measurable equivalence defined by an orthonormal basis is volume preserving.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 265 from the axioms · uses propext, Classical.choice, Quot.sound
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measureproof · cited by 10,939
- ENNRealstatement · cited by 9,879
- 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
- MeasureTheory.Measure.mapproof · cited by 858
Cited by2
Results whose statement or proof uses this declaration.
- OrthonormalBasis.measurePreserving_repr_symmproof · cited by 4
- OrthonormalBasis.measurePreserving_reprproof · cited by 0