Theorems · Theorem · dynamical systems
Ergodic.mem_extremePoints_measure_univ_eq
∀ {X : Type u_1} {m : MeasurableSpace X} {μ : MeasureTheory.Measure X} {f : X → X} [MeasureTheory.IsFiniteMeasure μ],
Ergodic f μ → μ ∈ Set.extremePoints ENNReal {ν | MeasureTheory.MeasurePreserving f ν ν ∧ ν Set.univ = μ Set.univ}- Defined in
- Mathlib.Dynamics.Ergodic.Extreme
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 220 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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 · 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.topproof · cited by 9,680
- Set.ofPredstatement and proof · cited by 6,101
- Set.univstatement and proof · cited by 3,945
- LT.lt.ne'proof · cited by 1,417
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- MeasureTheory.MeasurePreservingstatement and proof · cited by 259
- openSegmentproof · cited by 102
Cited by2
Results whose statement or proof uses this declaration.
- Ergodic.mem_extremePointsproof · cited by 1
- Ergodic.iff_mem_extremePoints_measure_univ_eqproof · cited by 0