Theorems · Theorem · dynamical systems
PreErgodic.aeconst_set
∀ {α : Type u_1} {m : MeasurableSpace α} {f : α → α} {μ : autoParam (MeasureTheory.Measure α) PreErgodic._auto_1},
PreErgodic f μ → ∀ ⦃s : Set α⦄, MeasurableSet s → f ⁻¹' s = s → Filter.EventuallyConst s (MeasureTheory.ae μ)- Defined in
- Mathlib.Dynamics.Ergodic.Ergodic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · 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
- MeasurableSetstatement · cited by 3,075
- MeasureTheory.aestatement · cited by 2,352
- Filter.EventuallyConststatement · cited by 93
- PreErgodicstatement and proof · cited by 19
Cited by7
Results whose statement or proof uses this declaration.
- QuasiErgodic.aeconst_set₀proof · cited by 3
- PreErgodic.smul_measureproof · cited by 2
- MeasureTheory.MeasurePreserving.preErgodic_of_preErgodic_semiconjproof · cited by 2
- PreErgodic.ae_empty_or_univproof · cited by 1
- PreErgodic.ae_mem_or_ae_notMemproof · cited by 1
- Ergodic.symmproof · cited by 1
- PreErgodic.of_iterateproof · cited by 0