Theorems · Theorem · dynamical systems

aeconst_of_dense_setOfPred_preimage_vadd_eq

∀ {M : Type u_1} [inst : TopologicalSpace M] {X : Type u_2} [inst_1 : TopologicalSpace X] [R1Space X]
  [inst_3 : MeasurableSpace X] [BorelSpace X] [inst_5 : VAdd M X] [ContinuousVAdd M X] {μ : MeasureTheory.Measure X}
  [MeasureTheory.IsFiniteMeasure μ] [μ.InnerRegular] [ErgodicVAdd M X μ] {s : Set X},
  MeasureTheory.NullMeasurableSet s μ →
    Dense {g | (fun x => g +ᵥ x) ⁻¹' s = s} → Filter.EventuallyConst s (MeasureTheory.ae μ)

Defined in

Mathlib.Dynamics.Ergodic.Action.OfMinimal

Cited by

3 results in Mathlib

Foundations

Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceR1SpaceMeasurableSpaceBorelSpaceVAddContinuousVAddMeasureTheory.IsFiniteMeasureMeasureTheory.Measure.InnerRegularErgodicVAdd