Theorems · Theorem · dynamical systems

PreErgodic.ae_empty_or_univ

∀ {α : Type u_1} {m : MeasurableSpace α} {s : Set α} {f : α → α} {μ : MeasureTheory.Measure α},
  PreErgodic f μ → MeasurableSet s → f ⁻¹' s = s → s =ᵐ[μ] ∅ ∨ s =ᵐ[μ] Set.univ

Defined in

Mathlib.Dynamics.Ergodic.Ergodic

Cited by

1 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound