Theorems · Theorem · measure theory

MeasureTheory.MeasurePreserving.measure_symmDiff_preimage_iterate_le

∀ {α : Type u_1} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} {f : α → α} {s : Set α},
  MeasureTheory.MeasurePreserving f μ μ →
    MeasureTheory.NullMeasurableSet s μ → ∀ (n : ℕ), μ (symmDiff s (f^[n] ⁻¹' s)) ≤ n • μ (symmDiff s (f ⁻¹' s))

Defined in

Mathlib.Dynamics.Ergodic.MeasurePreserving

Cited by

0 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace