Theorems · Theorem · measure theory
volume_preimage_coe
∀ {α : Type u_2} [inst : MeasureTheory.MeasureSpace α] {s t : Set α},
MeasureTheory.NullMeasurableSet s MeasureTheory.volume →
MeasurableSet t → MeasureTheory.volume (Subtype.val ⁻¹' t) = MeasureTheory.volume (t ∩ s)- Defined in
- Mathlib.MeasureTheory.Measure.Restrict
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasureTheory.MeasureSpace
Around this declaration
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Cites19
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
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Set.Elemproof · cited by 7,166
- Set.preimagestatement and proof · cited by 4,946
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- MeasureTheory.NullMeasurableSetstatement and proof · cited by 337
- Subtype.coe_injectiveproof · cited by 205
- MeasurableSet.nullMeasurableSetproof · cited by 155
- Set.image_preimage_eq_inter_rangeproof · cited by 121
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