Theorems · Theorem · dynamical systems

ErgodicSMul.aeconst_of_forall_preimage_smul_ae_eq

∀ {G : Type u_1} {α : Type u_2} {inst : SMul G α} {x : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  [self : ErgodicSMul G α μ] {s : Set α},
  MeasurableSet s → (∀ (g : G), (fun x => g • x) ⁻¹' s =ᵐ[μ] s) → Filter.EventuallyConst s (MeasureTheory.ae μ)

Defined in

Mathlib.Dynamics.Ergodic.Action.Basic

Cited by

1 results in Mathlib

Foundations

Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ErgodicSMul