Theorems · Theorem · measure theory
MeasureTheory.Measure.QuasiMeasurePreserving.preimage_iterate_ae_eq
∀ {α : Type u_1} {mα : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α} {f : α → α},
MeasureTheory.Measure.QuasiMeasurePreserving f μ μ → ∀ (k : ℕ), f ⁻¹' s =ᵐ[μ] s → f^[k] ⁻¹' s =ᵐ[μ] s- Cited by
- 4 results in Mathlib
- Foundations
- Depth 204 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.
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Set.preimagestatement and proof · cited by 4,946
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- Nat.iteratestatement and proof · cited by 740
- Filter.EventuallyEq.transproof · cited by 123
- Filter.EventuallyEq.reflproof · cited by 108
- MeasureTheory.Measure.QuasiMeasurePreservingstatement and proof · cited by 101
- Set.preimage_compproof · cited by 57
- Function.iterate_succproof · cited by 19
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.QuasiMeasurePreserving.image_zpow_ae_eqproof · cited by 0