Theorems · Theorem · measure theory
MeasureTheory.MeasurePreserving.preimage_null
∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β] {μa : MeasureTheory.Measure α}
{μb : MeasureTheory.Measure β} {f : α → β},
MeasureTheory.MeasurePreserving f μa μb → ∀ {s : Set β}, μb s = 0 → μa (f ⁻¹' s) = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Set.preimagestatement · cited by 4,946
- MeasureTheory.MeasurePreservingstatement and proof · cited by 259
- MeasureTheory.MeasurePreserving.quasiMeasurePreservingproof · cited by 41
- MeasureTheory.Measure.QuasiMeasurePreserving.preimage_nullproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.MeasurePreserving.singularPartproof · cited by 1