Theorems · Theorem · measure theory
volume_image_subtype_coe
∀ {α : Type u_2} [inst : MeasureTheory.MeasureSpace α] {s : Set α},
MeasurableSet s → ∀ (t : Set ↑s), MeasureTheory.volume (Subtype.val '' t) = MeasureTheory.volume t- Defined in
- Mathlib.MeasureTheory.Measure.Restrict
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasureTheory.MeasureSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasureTheory.Measurestatement · cited by 10,939
- ENNRealstatement · cited by 9,879
- Set.Elemstatement and proof · cited by 7,166
- Set.imagestatement · cited by 5,609
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- MeasureTheory.MeasureSpacestatement and proof · cited by 51
- MeasureTheory.Measure.Subtype.measureSpacestatement · cited by 10
- comap_subtype_coe_applyproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- unitInterval.volume_Iioproof · cited by 0