Theorems · Theorem · measure theory

MeasureTheory.MeasurePreserving.aeconst_preimage

∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β] {μa : MeasureTheory.Measure α}
  {μb : MeasureTheory.Measure β} {f : α → β},
  MeasureTheory.MeasurePreserving f μa μb →
    ∀ {s : Set β},
      MeasureTheory.NullMeasurableSet s μb →
        (Filter.EventuallyConst (f ⁻¹' s) (MeasureTheory.ae μa) ↔ Filter.EventuallyConst s (MeasureTheory.ae μb))

Defined in

Mathlib.Dynamics.Ergodic.MeasurePreserving

Cited by

1 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpace