Theorems · Theorem · dynamical systems

MeasureTheory.Measure.QuasiMeasurePreserving.birkhoffSum_ae_eq_of_ae_eq

∀ {α : Type u_1} {M : Type u_2} [inst : MeasurableSpace α] [inst_1 : AddCommMonoid M] {f : α → α}
  {μ : MeasureTheory.Measure α} {φ ψ : α → M},
  MeasureTheory.Measure.QuasiMeasurePreserving f μ μ → φ =ᵐ[μ] ψ → ∀ (n : ℕ), birkhoffSum f φ n =ᵐ[μ] birkhoffSum f ψ n

If observables φ and ψ are μ-a.e. equal then the corresponding birkhoffSum are μ-a.e. equal.

Defined in

Mathlib.Dynamics.BirkhoffSum.QuasiMeasurePreserving

Cited by

1 results in Mathlib

Foundations

Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceAddCommMonoid