Theorems · Theorem · measure theory
MeasureTheory.Measure.map_linearMap_addHaar_eq_smul_addHaar
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : MeasurableSpace E] [BorelSpace E]
[FiniteDimensional ℝ E] (μ : MeasureTheory.Measure E) [μ.IsAddHaarMeasure] {f : E →ₗ[ℝ] E},
LinearMap.det f ≠ 0 → MeasureTheory.Measure.map (⇑f) μ = ENNReal.ofReal |(LinearMap.det f)⁻¹| • μ- Cited by
- 3 results in Mathlib
- Foundations
- Depth 254 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites39
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
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- LinearMapstatement and proof · cited by 10,215
- ENNRealstatement · cited by 9,879
- MonoidHomstatement · cited by 3,629
- LinearEquivproof · cited by 3,317
- Continuousproof · cited by 2,592
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.map_addHaar_smulproof · cited by 6
- MeasureTheory.Measure.addHaar_preimage_linearMapproof · cited by 2
- MeasureTheory.Measure.LinearMap.quasiMeasurePreservingproof · cited by 1