Theorems · Theorem · dynamical systems
AddCircle.ergodic_zsmul_add
∀ {T : ℝ} [hT : Fact (0 < T)] (x : AddCircle T) {n : ℤ}, 1 < |n| → Ergodic (fun y => n • y + x) MeasureTheory.volume- Defined in
- Mathlib.Dynamics.Ergodic.AddCircle
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 282 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Factstatement and proof · cited by 2,726
- absstatement and proof · cited by 1,814
- one_smulproof · cited by 1,374
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- ne_of_gtproof · cited by 637
- AddSubgroup.zmultiplesstatement · cited by 493
- sub_add_cancelproof · cited by 344
- neg_smulproof · cited by 306
- MeasurableEquivproof · cited by 269
- smul_addproof · cited by 263
Cited by1
Results whose statement or proof uses this declaration.
- AddCircle.ergodic_nsmul_addproof · cited by 1