Theorems · Theorem · measure theory
Real.volume_preimage_mul_left
∀ {a : ℝ},
a ≠ 0 → ∀ (s : Set ℝ), MeasureTheory.volume ((fun x => a * x) ⁻¹' s) = ENNReal.ofReal |a⁻¹| * MeasureTheory.volume s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 249 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Set.preimagestatement · cited by 4,946
- absstatement and proof · cited by 1,814
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- ENNReal.ofRealstatement and proof · cited by 863
- Homeomorph.toMeasurableEquivproof · cited by 32
- MeasurableEquiv.map_applyproof · cited by 26
- Homeomorph.mulLeft₀proof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- Real.smul_map_diagonal_volume_piproof · cited by 1