Theorems · Theorem · dynamical systems
AddCircle.ergodic_add_left
∀ {p : ℝ} [inst : Fact (0 < p)] {a : AddCircle p}, Ergodic (fun x => a + x) MeasureTheory.volume ↔ addOrderOf a = 0- Defined in
- Mathlib.Dynamics.Ergodic.AddCircleAdd
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 279 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Factstatement and proof · cited by 2,726
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- AddSubgroup.zmultiplesstatement · cited by 493
- addOrderOfstatement · cited by 208
- AddCirclestatement and proof · cited by 189
- DenseRangeproof · cited by 164
- Ergodicstatement and proof · cited by 48
- AddCircle.denseRange_zsmul_iffproof · cited by 2
- ergodic_add_left_iff_denseRange_zsmulproof · cited by 1
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