Theorems · Theorem · dynamical systems

MeasureTheory.aeconst_of_forall_preimage_smul_ae_eq

∀ (G : Type u_1) {α : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : SMul G α]
  [ErgodicSMul G α μ] {s : Set α},
  MeasureTheory.NullMeasurableSet s μ →
    (∀ (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

2 results in Mathlib

Foundations

Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SMulErgodicSMul