Theorems · Theorem · measure theory
MeasureTheory.Measure.QuasiMeasurePreserving.preimage_ae_eq
∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {μa : MeasureTheory.Measure α}
{μb : MeasureTheory.Measure β} {f : α → β} {s t : Set β},
MeasureTheory.Measure.QuasiMeasurePreserving f μa μb → s =ᵐ[μb] t → f ⁻¹' s =ᵐ[μa] f ⁻¹' t- Cited by
- 5 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Set.preimagestatement · cited by 4,946
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- Filter.EventuallyEq.symmproof · cited by 408
- MeasureTheory.Measure.QuasiMeasurePreservingstatement and proof · cited by 101
- Filter.EventuallyEq.leproof · cited by 46
- Filter.EventuallyLE.antisymmproof · cited by 23
- MeasureTheory.Measure.QuasiMeasurePreserving.preimage_mono_aeproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.NullMeasurableSet.preimageproof · cited by 21
- MeasureTheory.Measure.QuasiMeasurePreserving.preimage_iterate_ae_eqproof · cited by 4
- MeasureTheory.Measure.set_prod_ae_eqproof · cited by 2
- MeasureTheory.Measure.QuasiMeasurePreserving.image_zpow_ae_eqproof · cited by 0