Theorems · Theorem · dynamical systems
Ergodic.of_mem_extremePoints_measure_univ_eq
∀ {X : Type u_1} {m : MeasurableSpace X} {μ : MeasureTheory.Measure X} {f : X → X} {c : ENNReal},
c ≠ ⊤ → μ ∈ Set.extremePoints ENNReal {ν | MeasureTheory.MeasurePreserving f ν ν ∧ ν Set.univ = c} → Ergodic f μGiven a constant c ≠ ∞, an extreme point of the set of measures that are invariant under f
and have total mass c is an ergodic measure.
- Defined in
- Mathlib.Dynamics.Ergodic.Extreme
- Cited by
- 2 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.
Cites45
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 and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- Set.ofPredstatement and proof · cited by 6,101
- Set.preimageproof · cited by 4,946
- Set.univstatement and proof · cited by 3,945
- mul_oneproof · cited by 3,885
- MeasurableSetproof · cited by 3,075
- Compl.complproof · cited by 2,925
Cited by2
Results whose statement or proof uses this declaration.
- Ergodic.of_mem_extremePointsproof · cited by 1
- Ergodic.iff_mem_extremePoints_measure_univ_eqproof · cited by 0