Theorems · Theorem · dynamical systems
MeasureTheory.ergodicSMul_iterateMulAct
∀ {α : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → α},
Measurable f → (ErgodicSMul (IterateMulAct f) α μ ↔ Ergodic f μ)- Defined in
- Mathlib.Dynamics.Ergodic.Action.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Set.preimageproof · cited by 4,946
- MeasurableSetproof · cited by 3,075
- MeasureTheory.aeproof · cited by 2,352
- Filter.EventuallyEqproof · cited by 1,912
- Measurablestatement and proof · cited by 1,499
- MeasureTheory.MeasurePreservingproof · cited by 259
- MeasurableSet.nullMeasurableSetproof · cited by 155
- Filter.EventuallyEq.reflproof · cited by 108
- Filter.EventuallyConstproof · cited by 93
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